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Find an equation for the line perpendicular to the tangent to the curve y = x^3-9x+5 at the...

Question:

Find an equation for the line perpendicular to the tangent to the curve {eq}y = x^3-9x+5 {/eq} at the point (3,5).

What is the smallest slope on the curve? At what point on the curve does the curve have this slope?

Find equations for the tangent to the curve where the slope is 18.

Equation of Tangent:

We have been given a cubic function and we have to find the equations of tangent and normal. We will do this by differentiation of the function. We will get the slope of the tangent. With its help we can find the slope of the normal and hence we can find the equation of the normal.

Answer and Explanation:

{eq}a)\text{Finding the slope of the tangent}\\ y'=3x^2-9\\ y'(3,5)=18\\ \text{Now that we have the slope of the tangent we can find the slope of...

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