given h(x)=x^3+x-1 on the interval[0,2], will there be a value p such that 0

Question

given h(x)=x^3+x-1 on the interval[0,2], will there be a value p such that 0<p<2 and h'(p)=5? Justify your answer. If your answer is yes, find p.

Raymond B. · Accepted Answer

take the derivative of h to get h' = 3x^2 +1, set it equal to 5, solve for x:  3x^2=4, x^2 = 4/3, x= 2/sqr3

given h(x)=x^3+x-1 on the interval[0,2], will there be a value p such that 0<p<2 and h'(p)=5? Justify your answer. If your answer is yes, find p.