What is the tangent of f(x)=log_{2}(2x^2+14),\at x=5 ?

The tangent of f(x)=log_{2}(2x^2+14),\at x=5 is y= 5/(16ln(2))x+6-(25)/(16ln(2))

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tangent of f(x)=log_{2}(2x^2+14),\at x=5

tangent of

f (x) = lo g_{2} (2 x^{2} + 14), at x = 5

y = \frac{5}{16 ln ( 2 )} x + 6 - \frac{25}{16 ln ( 2 )}

Solution steps

Find the tangent point:

(5, 6)

Find the slope of

f (x) = lo g_{2} (2 x^{2} + 14) : \frac{df ( x )}{d x} = \frac{2 x}{ln ( 2 ) ( x ^{2} + 7 )}

Compute the slope of

f (x) = lo g_{2} (2 x^{2} + 14)

x = 5 : m = \frac{5}{16 ln ( 2 )}

Find the line with slope m=

\frac{5}{16 ln ( 2 )}

and passing through

(5, 6) : y = \frac{5}{16 ln ( 2 )} x + 6 - \frac{25}{16 ln ( 2 )}

y = \frac{5}{16 ln ( 2 )} x + 6 - \frac{25}{16 ln ( 2 )}

x \to 2 lim (\frac{0}{4})

\frac{1}{x - 1}, 5

y = 8 x - x^{2}

\int (x + 4)^{\frac{1}{2}} d x

\frac{d y}{d x} = (2 x)

What is the tangent of f(x)=log_{2}(2x^2+14),\at x=5 ?
The tangent of f(x)=log_{2}(2x^2+14),\at x=5 is y= 5/(16ln(2))x+6-(25)/(16ln(2))