Question

How do you find the slope of a tangent line to the graph of the function `f(x) = 7x-5x^2` at (-2,-34)?

Answer 1

The slope of `f(x)=7x-5x^2` at `(x,y)=(-2,-34)` is `color(red)(27)`

Explanation:

The slope of a function is given by the derivative of the slope.

Given
`color(white)("XXX")f(x)=7x-5x^2`
the derivative (slope) is
`color(white)("XXX")f'(x)=7-10xcolor(white)("xxxx")`by applying the exponent rule

For the point `(x,y)=(-2,-34)`
(that is when `x=-2`)
the slope is
`color(white)("XXX")f'(-2)=7-10*(-2)=7+20=27`