Question

Help to find c and d:

Answer 1

the average acceletarion between 1 and 4:
\[\frac{ \Delta v }{ \Delta t }= \frac{ 4-(-2) }{ 4-1 }=\frac{ 6 }{ 3 }=2(m/s ^{2})\]
the instantaneous acceleration at 3:
-you have to find the slope of the tangent line, this tangent line pass through (2;-4) and (3;0) so the slope is \[\frac{ x_{1}-x _{_{0}} }{ y _{1}-y _{0} }=\frac{ 0-(-4) }{ 3-2 }=\frac{ 4 }{ 1 }=4m/s ^{2}\]
you can also find the derrivative, but you have to find the equation f(x) when \[x \rightarrow 3\] it is :
\[f (x)= 4x-12 \]then\[f \prime (x ) =4; and ; f \prime (3)=4m/s ^{2} \]