Question

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

Answer 1

`y=68x-235`

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`