What is the tangent of 2/(sqrt(1/4+h))-4 ?

The tangent of 2/(sqrt(1/4+h))-4 is y=-8/((4a_{0)+1)^{3/2}}h+(24a_{0}+4)/((4a_{0)+1)^{3/2}}-4

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tangent of 2/(sqrt(1/4+h))-4

tangent of

\frac{2}{\frac{1}{4} + h} - 4

y = - \frac{8}{( 4 a _{0} + 1 ) ^{\frac{3}{2}}} h + \frac{24 a _{0} + 4}{( 4 a _{0} + 1 ) ^{\frac{3}{2}}} - 4

Solution steps

Compute the tangent line to the general point

h = a_{0}

Find the tangent point:

(a_{0}, \frac{4}{1 + 4 a _{0}} - 4)

Find the slope of

y = \frac{2}{\frac{1}{4} + h} - 4 : \frac{d y}{d h} = - \frac{8}{( 4 h + 1 ) ^{\frac{3}{2}}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{8}{( 4 a _{0} + 1 ) ^{\frac{3}{2}}}

Find the line with slope m=

- \frac{8}{( 4 a _{0} + 1 ) ^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{4}{1 + 4 a _{0}} - 4) : y = - \frac{8}{( 4 a _{0} + 1 ) ^{\frac{3}{2}}} h + \frac{24 a _{0} + 4}{( 4 a _{0} + 1 ) ^{\frac{3}{2}}} - 4

y = - \frac{8}{( 4 a _{0} + 1 ) ^{\frac{3}{2}}} h + \frac{24 a _{0} + 4}{( 4 a _{0} + 1 ) ^{\frac{3}{2}}} - 4

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y = x^{4} e^{- x}, (1, \frac{1}{e})

\int \frac{1}{( 100 - x ^{2} ) ^{2}} d x

(- 2.3) (6.2)

\int \frac{6 x}{6 + x} d x

What is the tangent of 2/(sqrt(1/4+h))-4 ?
The tangent of 2/(sqrt(1/4+h))-4 is y=-8/((4a_{0)+1)^{3/2}}h+(24a_{0}+4)/((4a_{0)+1)^{3/2}}-4