Any help on these 2 questions would be greatly appreciated, I kinda know the differentiantion question but just wanna get the answer! thank you 

1 Answer

Top Answer

crmhaske's profile pic

crmhaske | College Teacher | (Level 3) Associate Educator

Posted on

For f) we will graph a=1 (black), a=2 (red), and a=3 (orange) to show what happens to the graph as a increases:

As you can see, as a increases the concavity of the function becomes tighter.  Furthermore, the sign of the second derivative of a function can tell you it's concavity (positive for concave up):




`a^xgt0` because a>0 and `ln(a)^2gt0`

Therefore, because f''(x)>0 the graph is concave up.

f) `f(x)=sin(x^2+2x)sqrt(2x-7)` find f'(x)

Use the product rule:

`u(x)=sin(x^2+2x) -gt u'(x)=(2x+2)cos(x^2+2x)`