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

Question

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yes