What is the equation of the tangent line of f(x)=x at x=25?

Explanation:Rewrite the function f(x)=xas f(x)=x12differentiating : f′(x)=12x−12Require the gradient (m) and the coordinates ( a , b ), a point on the line, to obtain the equation of the tangent.m=f′(25)=12×(25)−(12)=12(25)12=12×5=110and f(25)=25=5Equation of tangent is y - b = m(x - a ) where m=110and (a , b ) = (25 , 5 )ie y−5=110(x−25)multiply both sides of the equation by 10 to eliminate fraction.10y−50=x−25⇒10y−x−25=0

Answered: "What is the equation of the tangent line..."

High School
Calculus and Analysis
Calculus 1
Derivatives

Oxinailelpels3t14

Answered question

2022-03-25

What is the equation of the tangent line of

f (x) = \sqrt{x}

at x=25?

Answer & Explanation

ron4d3ozip7

Beginner2022-03-26Added 9 answers

Explanation:
Rewrite the function

f (x) = \sqrt{x}

f (x) = x^{\frac{1}{2}}

differentiating :

f^{'} (x) = \frac{1}{2} x^{- \frac{1}{2}}

Require the gradient (m) and the coordinates ( a , b ), a point on the line, to obtain the equation of the tangent.

m = f^{'} (25) = \frac{1}{2} \times {(25)}^{- (\frac{1}{2})} = \frac{1}{2 {(25)}^{\frac{1}{2}}} = \frac{1}{2 \times 5} = \frac{1}{10}

and

f (25) = \sqrt{25} = 5

Equation of tangent is y - b = m(x - a ) where

m = \frac{1}{10}

and (a , b ) = (25 , 5 )
ie

y - 5 = \frac{1}{10} (x - 25)

multiply both sides of the equation by 10 to eliminate fraction.

10 y - 50 = x - 25 \Rightarrow 10 y - x - 25 = 0

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