Question

Find the slope-predictor formula and write an equation for the line tangent to (a, f(a)) for f(x) = -2x^2+3x-7

Answer 1

is that what they are calling derivatives now? slope-predictor formula??

Answer 2

\[f(x)=-2x^2+3x-7\]
\[f'(x)=-4x+3\] so
\[f'(a)=-4a+3\] and that his the slope

Answer 3

then use point - slope formula to find the equation of the line:
\[y-y_1=m(x-x_1)\] with
\[x_1=a, y_1=f(a), m=(-4a+3)\]

Answer 4

you get
\[y-f(a)=(-4a+3)(x-a)\] and then some algebra

Answer 5

are you perhaps supposed to find
\[f'(a)\] by hand using
\[\lim_{x\rightarrow a}\frac{f(a)-f(x)}{a-x}\]?

Answer 6

yes