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

Example for articulate reasons and construct arguments, A Class 4 teacher w...

A Class 4 teacher was going to teach her class fractions. At the beginning of the term she asked the children, "If you had three chocolates, and wanted to divide them equally among

Distinct eigenvalues, It's now time to do solving systems of differential e...

It's now time to do solving systems of differential equations. We've noticed that solutions to the system, x?' = A x? It will be the form of, x? = ?h e l t Here l and

Constructions, Draw a line segment AB of length 4.4cm. Taking A as centre, ...

Draw a line segment AB of length 4.4cm. Taking A as centre, draw a circle of radius. 2cm and taking B as centre, draw another circle of radius 2.2cm. Construct tangents to each cir

Binormal vector - three dimensional space, Binormal Vector - Three Dimensio...

Binormal Vector - Three Dimensional Space Next, is the binormal vector.  The binormal vector is illustrated to be, B → (t) = T → (t) * N → (t) Since the binormal vecto

Example of quadratic polynomial, Factor following.                    x ...

Factor following.                    x 2 - 20 x + 100 Solution In this case we've got three terms & it's a quadratic polynomial.  Notice down as well that the constant

Which number falls among 5.56 and 5.81, Which number falls among 5.56 and 5...

Which number falls among 5.56 and 5.81? If you add a zero to the end of 5.6 to get 5.60, it is simpler to see that 5.56

Calculate the amount of money a person has left after death, When Ms. Jones...

When Ms. Jones retired, she received a lump sum of $1,000,000 from her pension plan.  She then invested this sum in an annuity account that would pay her an equal amount at the end

G .E matrix, using the g.e matrix, how can you turn an unattractive product...

using the g.e matrix, how can you turn an unattractive product to be attractive

Trigonometry, 1-tan^2 A/1+tan^2 = cos A - sinA/cos A

1-tan^2 A/1+tan^2 = cos A - sinA/cos A

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