Solve the following.

Question

Find f'(2) and f''(2) if f(x)=-2x^3+8x^-1+3x.

Answer 1

Solve the following.

Find f'(2) and f''(2) if f(x)=-2x³+8x^-1+3x

f'(x)=-2(3x^3-1)+8(-1)(x^-1-1)+3=-6x²-8x^-2+3

f'(2)=-6(2)²-8/(2)²+3=-24-2+3=-23

f'(x)=-6x²-8x^-2+3

f''(x)=-6(2x^2-1)-8(-2)x^-2-1=-12x+16x^-3

f''(2)=-12(2)+16/2³=-24+2=-22

Solution:

f'(2)=-23

f''(2)=-22

Answer 2

f'(x) = 6x^2 - 8x^(-2) + 3

f''(x) = 12x + 16x^(-3)

f'(2) = 24 + 3 - 2 = 25

f''(2) = 24 + 2 = 26

Answer 3

f(x)=-2x³ + 8x^-1 + 3x

f '(x) = -6 x² + (-1)(8)x^-2 + 3

f ' (x) = -6x² - 8x^-2 + 3

f ''(x) = -12x + 16x^-3

f '(2) = -6(2)² - 8(2)^-2 + 3 = -24 - 2 + 3 = -23

f ''(2) = -12(2) + 16(2)^-3 = -24 + 2 = -22