# Equations of Tangent lines and Intercepts in Terms of a Variable

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Let f(x) = a(7-x^2) where a is not equal 0

(a) find, in terms of a, the equation of the line tangent to the curve at x = -1 (use point slope)

(b) find, in terms of a, the y intercept of the tangent line at x = -1

(c) find the x intercept of the tangent line at x=-1

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#### Solution Preview

Let f(x) = a(7-x^2) where a is not equal 0

(a) find, in terms of a, the equation of the line tangent to the curve at x = -1 (use pt slope)

Solution. Since f'(x)=-2ax, the slope at x=-1 is given by

f'(-1)=-2a*(-1)=2a

When x=-1, then ...

#### Solution Summary

This solution provides equations of tangent lines and intercepts that are expressed in terms of a variable. The solution is detailed and well presented.

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