Let f(x) = 4x^5/4 + 6x^3/2 + 2x. Find the following.

Question

(a) f '(1)

(b) f '(16)

Answer 1

Find f'(x) by the power rule: multiply the coefficient by the power and subtract the power by 1.

f'(x) = 4(5/4)x^5/4-1 + 6(3/2)x^3/2-1 + 2(1)x^1-1 = 5x^1/4 + 9x^1/2 + 2

a) f'(1) means use the first derivative and let x = 1

f'(1) = 5x^1/4 + 9x^1/2 + 2 = 5(1)^1/4 + 9(1)^1/2 + 2 = 16

b) f'(16) means use the first derivative and let x = 16

f'(16) = 5x^1/4 + 9x^1/2 + 2 = 5(16)^1/4 + 9(16)^1/2 + 2 = 48