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5. The gradient of the tangent line to the graph of f(x)= 2x^2 + kx - 3 at x = -1 is 1. Find the value of k

5 The gradient of the tangent line to the graph of fx 2x2 kx 3 at x 1 is 1 Find the value of k class=

Respuesta :

LammettHash

The gradient of the tangent line to [tex]y(x)[/tex] at [tex](c,y(c))[/tex] is given by the value of the derivative at [tex]x=c[/tex]. We have

[tex]f(x)=2x^2+kx-3\implies f'(x)=4x+k[/tex]

We're told that [tex]f'(-1)=1[/tex]. Then

[tex]1=4(-1)+k\implies k=5[/tex]

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