Question

If f ( x ) = 4 x 2 − 2 x + 3 f ( x ) = 4 x 2 - 2 x + 3 , find f ' ( − 5 ) f ′ ( - 5 ) . Use this to find the equation of the tangent line to the parabola y = 4 x 2 − 2 x + 3 y = 4 x 2 - 2 x + 3 at the point ( − 5 , 113 ) ( - 5 , 113 ) . The equation of this tangent line can be written in the form y = m x + b y = m x + b where m m is: and where b b is:

Answer 1

$\bf f(x)=4x^2-2x+3\implies \left.\cfrac{dy}{dx}=8x-2 \right|_{x=-5}\implies -42 \\\\ -------------------------------\\\\ (-5,113)\qquad \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-113=-42[x-(-5)] \\\\\\ y-113=-42(x+5)\implies y-113=-42x-210 \\\\\\ y=-42x-97$