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Need help with derivative?

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Need help with derivative?

The tangent line to the graph of a function f at the point x=7 is y=5x−34. Find the tangent line to the graph of y=xf(x) at x=7. Put your answer into slope-intercept form.

 
 
asked Feb 19, 2015 in CALCULUS by anonymous
reshown Feb 19, 2015 by goushi

1 Answer

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Step 1 :

Tangent line equation is image.

At image, image.

Tangent line equation is image.

Differentiate the above equation with respect to image.

image.

Step 2 :

The curve equation is image.

Considering the function as image.

Differentiate the curve with respect to image.

image.

Evaluating image at image.

image.

image.

Derivative of the function is the slope of the tangent line.

The tangent line to the graph image at image is the line with slope 36 and passing through the point image.

Point-slope form of a line equation is image.

Let the point is image and the slope is image.

Substitute the corresponding values in point-slope form.

image

The tangent line equation is image.

Solution :

The tangent line equation is image.

answered Feb 20, 2015 by lilly Expert

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