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(a) Find the slope of `f(x) = 4x-2x^2` at the point `(-3, -30)`.
`m=`
(b) Find an equation for the line tangent at the point `(-3, -30)` in slope-intercept form.
`y=`
To determine the slope of the tangent line to the curve `f(x) = 4x-2x^2` at the point `(-3, -30)`, use the definition of the tangent slope `m_{\tan}=\underset{x o a}{\lim}\dfrac{f(x)-f(a)}{x-a}`. This calculated slope will be used to write the equation of the tangent line in slope-intercept form `y=mx+b`, where `m` is the slope at the point and `b` can be found by substituting the coordinates of the point into the equation.
Get help:
Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity
16
Box 2: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question
`16x+18`