Question

Find an equation of the tangent line to f(x) = 5x2 − 2x + 10 at x = 7.

Answer 1

Answer:

$y=68x-235$

Step-by-step explanation:

$f(x) = 5x^2-2x + 10$

Differentiate:

$\implies f'(x)=10x-2$

Substitute $x=7$ into $f'(x)$:

$\implies f'(7)=10(7)-2=68$

Therefore, 68 is the gradient of the tangent line at x=7:

$\implies y-y_1=68(x-x_1)$

when $x=7$, $y=5(7)^2-2(7)+10=241$

$\implies y-241=68(x-7)$

$\implies y=68x-235$