Differentiate the function and find the slope of the tangent line at the given value of the independent variable
$s = t^{3} - t^{2}, t = - 6$

Answer

Expert–verified

Hide Steps

Answer

Final Answer: The slope of the tangent line at $t = - 6$ is $120$

Steps

Step 1 ：Given the function $s = t^{3} - t^{2}$ and $t = - 6$

Step 2 ：Differentiate the function to find $d s / d t$ . The derivative of $t^{3}$ is $3 t^{2}$ and the derivative of $t^{2}$ is $2 t$ . So, $d s / d t = 3 t^{2} - 2 t$

Step 3 ：Substitute $t = - 6$ into $d s / d t$ to find the slope of the tangent line at that point. The slope is $3 (- 6)^{2} - 2 (- 6) = 120$

Step 4 ：Final Answer: The slope of the tangent line at $t = - 6$ is $120$

Differentiate the function and find the slope of the tangent line at the given value of the independent variables=t3−t2,t=−6

Answer

Popular Problems

Differentiate the function and find the slope of the tangent line at the given value of the independent variable
$s = t^{3} - t^{2}, t = - 6$