F(x) = 3x + x3 x > 0
a) Differentiate to find f'(x)
Given that f'(x) = 15,
b) Find the value of x

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

solving

now solving

Thus, the expression becomes

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value  f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 =  3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

Thus, the value of x will be:

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .