5 +1/4 f = 5 + f/4
^ means "to the power of" F ^ 2 + 4 = 5 ^ 2 F ^2 +4 = 25 F ^2+4 -4 = 25 -4 F^2 = 21 F = (square root of 21)
f+4(f-2)
If f(x) = 2 - 3x then f(4) = 2 - 3(4) so since 3 times 4 is 12, then f(4) = 2 - 12 which means f(4) = -10 Easy!
f(x)=x2-x3 f(2) = 4-8 = -4 f'(x) =2x-3x2 f'(2) = 4-12=-8 f''(x) = 2 -6x f''(2)= -10 f'''(x)= -6 f(n)(x) = 0 for all n > 3. f(x) = f(2) + (x-2) f'(2) / 1! + (x-2)2 f''(2) /2! + (x-2)3 f'''(2)/3! + . . . f(x) = -4 -8(x-2) -10(x-2)22/2-6(x-2)3/6 + 0 + 0 + ... f(x) = -4 -8(x-2) -5(x-2)2 - (x-2)3
4/5 (4 + f) = 4(4+f)/5
5 +1/4 f = 5 + f/4
The answer is 6. If you follow the circle of fifths, starting with C you have C 0 G 1 D 2 A 3 E 4 B 5 F# 6
^ means "to the power of" F ^ 2 + 4 = 5 ^ 2 F ^2 +4 = 25 F ^2+4 -4 = 25 -4 F^2 = 21 F = (square root of 21)
f+4(f-2)
f(x) = 2 * 2 - x + 9 f(-4) = 2 * 2 -(-4) + 9 f(-4) = 4 + 4 + 9 = 17
If f(x) = 2 - 3x then f(4) = 2 - 3(4) so since 3 times 4 is 12, then f(4) = 2 - 12 which means f(4) = -10 Easy!
f(x)=x2-x3 f(2) = 4-8 = -4 f'(x) =2x-3x2 f'(2) = 4-12=-8 f''(x) = 2 -6x f''(2)= -10 f'''(x)= -6 f(n)(x) = 0 for all n > 3. f(x) = f(2) + (x-2) f'(2) / 1! + (x-2)2 f''(2) /2! + (x-2)3 f'''(2)/3! + . . . f(x) = -4 -8(x-2) -10(x-2)22/2-6(x-2)3/6 + 0 + 0 + ... f(x) = -4 -8(x-2) -5(x-2)2 - (x-2)3
F(x)=x^2-5x+4
f(n) = (n² + n) / 2 f(1) = (1² + 1) / 2 = 1 f(2) = (2² + 2) / 2 = 3 f(3) = (3² + 3) / 2 = 6 f(4) = (4² + 4) / 2 = 10 f(5) = (5² + 5) / 2 = 15 f(6) = (6² + 6) / 2 = 21
Here's the graph:
It is f(x) = -x2 or (-x)2, whichever you intended.