Do First U4 Day 45

Is the above function differentiable for all values of x? Why?

• Yes, the slope of the tangent line can be calculated for all values of x.

• Yes, the function is continuous for all values of x so the function is differentiable.

• No, the function has a sharp turn in the first quadrant so if is not differentiable.

• No, the function is discontinuous so it is not differentiable.

Is the function is the following graph differentiable at x = 0? Why?

• Yes. The limit from the left and right of 0 both approach 0.

• No, $\lim_{x\rightarrow0}\left|x\right|\$ does not exist.

• No, $\lim_{h\rightarrow0}\frac{\left(\left|x+h\right|-\left|x\right|\right)}{h}$ does not exist.

• Yes, the function is differentiable because there is a constant rate of change of -1 from $\left(-\infty,0\right)$ and 1 from $\left(0,\infty\right)$ .

Given the following _____________line, find the instantaneous rate of change at  $x=1$  .

• secant,  $2$  

• tangent,  $2$  

• secant ,

   $\frac{1}{2}$  

• tangent,  $\frac{1}{2}$  

Given the following graph with tangent lines, at which

x-value is the derivative equal to zero?

•  $x=-8$  

•  $x=-5$  

•  $x=-1.7$  

•  $x=1$  

Find the average rate of change on the interval  $\left[a,a+h\right]$  

•  $\left(\frac{f\left(a+h\right)-f\left(a\right)}{a}\right)$  

•  $\left(\frac{f\left(a+h\right)-f\left(a\right)}{h}\right)$  

•  $\left(\frac{f\left(a\right)-f\left(a+h\right)}{h}\right)$  

•  $\frac{f\left(a+h\right)}{f\left(a\right)}$