A differentiable function is known to satisfy p'(x)=24x^ 5 for all x>0

MATHEMATICS · Multi-part · A Level · Mathematics · Integration · Integration

Problem

A differentiable function

p

is known to satisfy

p'(x)=24x^{5}\quad\text{for all }x>0.

In addition,

p(1)=10

. Parts: (a) Determine the value of the exponent

r

such that a power function of the form

x^{r}

would have the given derivative structure. (b) Using your result from part (a), find an explicit formula for

p(x)

. Show all antiderivative steps and verify that the function satisfies the initial condition.