Question

Asked Jan 15, 2020

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Find the area of the region bounded by the parabola *y* = 4*x*^{2}, the tangent line to this parabola at (3, 36), and the *x*-axis.

Step 1

The equation of the parabola is given by *y* = 4*x*^{2}.

Differentiate *y* = 4*x*^{2} with respect to *x* as follows.

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.

Step 3

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

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