0
$\begingroup$

I need to answer the question in the title for this function graph.

[Enter image description here]

I see that the derivative is positive in $3$ segments of the graph, and thinking about it as roughly $\frac{\bigtriangleup y} {\bigtriangleup x}$ it should be have points where derivative is $2$ or more in the first $2$ segments where the function grows.

But I don't know where to go from here and how to find the exact number of points.

$\endgroup$
  • $\begingroup$ It looks like the derivative is greater than 2 at an infinite number of points. $\endgroup$ – Carser May 9 '16 at 11:43
  • $\begingroup$ @Jed maybe but the question is about points where it equals 2. Also, the answer is supposed to be an integer $\endgroup$ – dvornik May 9 '16 at 11:49
0
$\begingroup$

Hint $1:$ The tangent at any point on the graph gives the derivative at that point.

Hint $2:$ The derivative is zero at exactly $5$ points in the given range.

Hint $3:$ Since the function is continuous, by Intermediate Value Theorem, there must be some $c$ between $a$ and $b$, such that $f(c)=\frac{f(b)-f(a)}{b-a}$

Can you take it from here? (Answer is $2$)

$\endgroup$
0
$\begingroup$

Hint: The definition of the derivate is

A formula for the coefficient of the tangent.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.