To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (36, 6), we know that (36, 6) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x

Step-by-step explanation:

Given

----- the equation of the curve

Required

The slope of f(x)

The slope (m) is calculated using:

implies that:

So, we have:

If ; then:

So, we have:

Multiply by:

Expand the numerator

Collect like terms

Cancel out h

implies that we substitute 0 for h;

So, we have:

Hence, the slope is 1/12

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1