Calculus can be used to find the slope of the line tangent to a curve. The slope of the tangent to the curve $y = f ( x ) \text { at } x = a$ is f'(a). Use f'(x) to find the slope of the tangent to $y = f ( x )$ at the given value of x.
-The derivative of a function can be used to find the slope of the line tangent to its graph. If the slope of the line tangent to the graph of $f ( x ) = - x ^ { 3 } + 7$ at $( 3 , - 20 )$ is $- 27$, write the equation of this tangent line.
A) $y = - 27 x + 47$
B) $\mathrm { y } = - 27 \mathrm { x } - 61$
C) $\mathrm { y } = - 27 \mathrm { x } - 47$
D) $y = - 27 x + 61$

Question

Quizplus · Accepted Answer

The slope of the tangent line is -27, and it passes through the point (3, -20). Using the point-slope form $y - y_1 = m(x - x_1)$, we get $y + 20 = -27(x - 3)$. Simplifying gives $y = -27x + 61$.

Calculus Can Be Used to Find the Slope of the Line