Asked Jan 15, 2020

Find the area of the region bounded by the parabola y = 4x2, the tangent line to this parabola at (3, 36), and the x-axis.


Expert Answer

Step 1

The equation of the parabola is given by y = 4x2.

Differentiate y = 4x2 with respect to x as follows.

Calculus homework question answer, step 1, image 1
Step 2

Now the point (3,36) lies on the tangent line and its slope is 24.

Equation of the tangent line is computed as shown below.

Calculus homework question answer, step 2, image 1
Step 3

The graph of the parabola and tangent line is shown below.

Calculus homework question answer, step 3, image 1

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