0
What is the slope of the tangent line to y equals x3 at x equals 4?
Wiki User
∙ 12y ago
Do you mean y=3x or y=x3?
I'll assume it's the latter.
The first method to solving this is the easiest, the chain rule.
Multiply the coefficient by the value of the exponent and reduce the exponent by 1. (f(x)=nAxn-1)
You get y=3x2
Therefore, f(4)=3(42)
f(4)=48
The longer method of solving this goes as follows:
Your tangent formula is f'(x)=limh->0(f(x+h)-f(x))/h
We know that f(x)=x3 so f(x+h)=(x+h)3
When we put this in the formula we have:
f'(x)=limh->0((x+h)3-x3)/h
f'(x)=limh->0((x+h)(x+h)(x+h)-x3)/h
f'(x)=limh->0((x2+2hx+h2)(x+h)-x3)/h
f'(x)=limh->0(x3+x2h+2x2h+2xh2+xh2+h3-x3)/h
f'(x)=limh->0(3x2+3xh+h2)
f'(x)=3x2+3x(0)+(02)
f'(x)=3x2
And from there again we sub in 4 for x.
f'(4)=3(42)
f'(4)=48
Wiki User
∙ 12y ago
Add your answer:
Earn +20 pts
An equation of the line tangent to the graph of y equals x3 plus 3x2 plus 2 at its point of inflection is?
(a) y = -3x + 1
How do you find the rate of change?
Differentiation of the function would give you an instantaneous rate of change at one point; the tangent line. Repeated differentiation of some functions would give you many such points. f(x) = X3 = d/dx( X3) = 3X2 =======graph and see
X3 64 343?
The math problem X3 times 64/334 equals 4/7. Getting this answer you will first have to find the value of X.
What is the slope of the curve x-cubed minus 2x plus 5 at a point x y on the curve?
The derivative of x3-2x+5 is 3x2- 2. This is its slope at a point x,y.
Which statement best describes the function below fx equals x3-x2-9x 9?
A cubic.
An equation of the line tangent to the graph of y equals x3 plus 3x2 plus 2 at its point of inflection is?
(a) y = -3x + 1
How do you find the equation of the tangent line to a given equation fx equals x3 plus 3x2-5 that is perpendicular to a given equation 2x-6y plus 1 equals 0 with no x values given?
First consider the given line: 2x - 6y + 1 = 0Subtract (2x+1) from each side: -6y = -2x - 1Divide each side by -6: y= 1/3 x + 1/6The slope of this line is 1/3, so any line perpendicular to it has a slope of -3 .Now let's find places on the function where its slope is -3 :f(x) = x3 + 3x2 - 5The slope of the tangent to the function at every point is the value ofits first derivative at that point.f'(x) = 3x2 + 6x and we want it to be = -3 .3x2 + 6x + 3 = 0Divide both sides by 3 to make it neater and easier:x2 + 2x + 1 = 0Either use the quadratic equation to solve this, or else notice thatit's a perfect square ... (x+1)2 = 0, sox = 1That's the x-value on the graph of the function where the slope of thetangent to the function is -3.Substitute this 'x' back into the original function to find the corresponding 'y' value.Then you'll have the 'x' and 'y' coordinates of the point on the graph of the functionwhere the tangent has the slope of -3 .Now you have the slope and one point on the line that solves the problem,and finding the equation of the line should now be a piece o' cake.
How do you graph y equals x3?
The graph is a diagonal line with a slope of 1, passing through the x-axis at (3, 0) and the y-axis at (0, -3), extending from the lower left to the upper right.
What is the slope x-2?
If you're referring to the line: y = x - 2 Then it has a slope of zero. On the other hand, if you're referring to the curve: y = x-2 Then at any x position, it has a slope of -2/x3.
What are three ways of finding the slope?
1. Change in y over change in x. For a linear equation, this is just m = (y2-y1)/(x2-x1) where (x1,y1), (x2,y2) are any two points on the line. 2. Evaluating the tangent of the angle relative to horizontal. For example, if a ramp has a 10 degree angle above horizontal, then the slope is tan(10). 3. For any differentiable function y in terms of x, dy/dx gives the expression for the slope of a tangent line through a point on y. If y = x3+1, then dy/dx = 3x2, and at the point (1,2), dy/dx = 3, so the slope at this point is 3. Finding the derivative of a function is very similar to finding the slope of two points on a function that are infinitely close together.
How do you find the rate of change?
Differentiation of the function would give you an instantaneous rate of change at one point; the tangent line. Repeated differentiation of some functions would give you many such points. f(x) = X3 = d/dx( X3) = 3X2 =======graph and see
How do you find the instantaneous rate of change?
Differentiation of the function would give you an instantaneous rate of change at one point; the tangent line. Repeated differentiation of some functions would give you many such points. f(x) = X3 = d/dx( X3) = 3X2 =======graph and see
What is the slope and the y intercept of the equation x3?
If you mean: y = x+3 then the slope is 1 and the y intercept is 3
What is x in x3 equals 5.231010?
x^(3) = 5.1231010 Take the cube root Hence x = 5.231010^(1/3) x = 1.735915243
What x what equals 63?
what x3 equals 63 is:21x3=63
What is x to the third power and then to the second power?
That's the same as x3 times x3 which equals x6
Whats y3+x3+z3 equals to?
3xyz
