What are the minimum and maximum values of f(x) on the interval [1,3]?

[naspek]

Let f(x) = 5x^3 +4x + 8

(i) find f'(x)

answer--> 15x^2 + 4

(ii) Show that f(x) is increasing on (-\infty,\infty)

answer--> don't know how to prove it..

(iii)Hence find the minimum and maximum value of f(x) on the closed
interval [1,3]

answer-->please guide me to start aswering this question..

 

[phsopher]

A function is increasing if the derivative is greater than zero. If the function is increasing then what are its maximum and minimum values in a closed interval?

 

[naspek]

should i search for critical points first?

 

[phsopher]

If you like. But you can see directly from the expression of the derivative that it's never equal to zero.