What is the tangent of f(x)=-7x^2+3x,\at x=4 ?

The tangent of f(x)=-7x^2+3x,\at x=4 is y=-53x+112

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tangent of f(x)=-7x^2+3x,\at x=4

tangent of

f (x) = - 7 x^{2} + 3 x, at x = 4

y = - 53 x + 112

Solution steps

Find the tangent point:

(4, - 100)

Find the slope of

f (x) = - 7 x^{2} + 3 x : \frac{df ( x )}{d x} = - 14 x + 3

Compute the slope of

f (x) = - 7 x^{2} + 3 x

x = 4 : m = - 53

Find the line with slope m=

- 53

and passing through

(4, - 100) : y = - 53 x + 112

y = - 53 x + 112

x \to 2 lim (x^{2} - 2 x)

4 x^{2} y^{^{''}} + 8 x y^{^{'}} - 3 y = 0

x \to 0 - lim (\frac{sin ( x )}{x})

\frac{d}{d x} (sin (x) - cos^{2} (x))

y^{^{''}} + 16 y = x e^{3 x}

What is the tangent of f(x)=-7x^2+3x,\at x=4 ?
The tangent of f(x)=-7x^2+3x,\at x=4 is y=-53x+112