Find the slope of the curve at the indicated point.
-Find an equation of the tangent to the curve $f ( x ) = 2 x ^ { 2 } - 2 x + 1$ that has slope 2 .
A) $y = 2 x + 2$
B) $y = 2 x + 1$
C) $y = 2 x$
D) $y = 2 x - 1$

Question

Quizplus · Accepted Answer

To find the slope of the curve, we take the derivative of the function: 
$$f'(x) = 4x - 2$$
To find where the slope is equal to 2, we set $f'(x) = 2$ and solve for $x$: 
$$4x - 2 = 2 \Rightarrow x = 1$$
So the slope of the curve at the point $(1,1)$ is $f'(1) = 4(1) - 2 = 2$.

Now that we know the point and slope of the tangent line, we can use point-slope form to find an equation of the line: 
$$y - 1 = 2(x - 1)$$
Simplifying, we get 
$$y = 2x - 1$$
So the answer is D.

Find the Slope of the Curve at the Indicated Point f(x)=2x2−2x+1f ( x ) = 2 x ^ { 2 } - 2 x + 1f(x)=2x2−2x+1

Find the Slope of the Curve at the Indicated Point $f ( x ) = 2 x ^ { 2 } - 2 x + 1$