If $f(x) = 3x^2 -5x$ , how do you find and use it to find an equation of the tangent line at the point (2, 2)? I have no idea how to approach this.?

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Answer 1 · 2015-04-12T16:14:43

What is it you are asked to find and use?

Answer 2 · 2015-04-12T18:27:49

(I'm assuming the "and use it to find" was redundant)

If $f(x) = 3x^2-5x$

Then the derivative (which gives the slope of the tangent) is
$f'(x) =6x-5$

(using $y$ in place of $f(x)$ for simplicity)

The slope of the tangent at $(x_1,y_1) = (2,2)$
is
$m=6(2)-5 = 7$ (substituting $2$ for $x$ in the expression for $f'(x)$

The slope-point form of an equation for the line is
$(y-y_1) = m(x-x_1)$

or, in this case
$(y-2) = 7(x-2)$
which simplifies as
$y = 7x -12$

If f(x) = 3x^2 -5xf(x) = 3x^2 -5x, how do you find and use it to find an equation of the tangent line at the point (2, 2)? I have no idea how to approach this.?