Determine equation of tangent line, Mathematics

Assignment Help:

Determine equation of the tangent line to f (x) = 4x - 8 √x  at x = 16 .

Solution : We already know that the equation of a tangent line is specified by,

                           y = f ( a ) + f ′ ( a ) ( x - a )

Hence, we will have the derivative of the function (don't forget to get rid of the radical).

f ( x ) = 4x - 8x ½    ⇒   f ′ ( x ) = 4 - 4x -1/2  = 4 -  4/x 1/2

Again, notice as well that we remove the negative exponent in the derivative solely for the sake of the evaluation.  All we have to do then is evaluate the function & the derivative at the point in question, x = 16 .

f (16) = 64 - 8 ( 4) = 32                                                       f ′ ( x )  = 4 - 4 /4= 3

Then the tangent line is,

y = 32 + 3( x -16) = 3x -16

 


Related Discussions:- Determine equation of tangent line

Spring force, Spring, F s We are going to suppose that Hooke's Law wil...

Spring, F s We are going to suppose that Hooke's Law will govern the force as the spring exerts on the object. This force will all the time be present suitably and is F s

Physics of medical imaging, A radiograph is made of an object with a width ...

A radiograph is made of an object with a width of 3 mm using an x-ray tube with a 2 mm focal spot at a source-to-film distance of 100 cm. The object being imaged is 15 cm from the

Inequalities, I want to complete my assignment, please explain me what is I...

I want to complete my assignment, please explain me what is Inequalities?

What is the cost to generate, The production costs per week for generating ...

The production costs per week for generating x widgets is given by, C ( x ) = 500 + 350 x - 0.09 x 2 ,         0 ≤ x ≤ 1000 Answer following questions.  (a) What is the c

Geometry, a figure is made of a rectangle and an isosceles right triangle. ...

a figure is made of a rectangle and an isosceles right triangle. the rectangle has sides of 6 in. and 3 in. one of the short sides of the rectangle is also one of the legs of the r

Function composition, Function composition: The next topic that we have to...

Function composition: The next topic that we have to discuss here is that of function composition. The composition of f(x) & g(x) is ( f o g ) ( x ) = f ( g ( x )) In other

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd