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

Decision-making under conditions of uncertainty, Decision-Making Under Cond...

Decision-Making Under Conditions of Uncertainty With decision making under uncertainty, the decision maker is aware of different possible states of nature, but has insufficient

Estimate the cost of the car, Kyra receives a 5% commission on every car sh...

Kyra receives a 5% commission on every car she sells. She received a $1,325 commission on the last car she sold. What was the cost of the car? Use the proportion part/whole =

Simultaneous equations by substitution, Simultaneous equations by substitut...

Simultaneous equations by substitution: Solve the subsequent simultaneous equations by substitution. 3x + 4y = 6      5x + 3y = -1 Solution: Solve for x: 3x = 6

Determine the height of building, A 20-foot light post shows a shadow 25 fe...

A 20-foot light post shows a shadow 25 feet long. At the similar time, a building nearby casts a shadow 50 feet long. determine the height of building? a. 40 ft b. 62.5 ft

Marginal cost & cost function, Marginal cost & cost function  The cost ...

Marginal cost & cost function  The cost to produce an additional item is called the marginal cost and as we've illustrated in the above example the marginal cost is approxima

Determine differential equation from direction field, Thus, just why do we ...

Thus, just why do we care regarding direction fields? Two nice pieces of information are there which can be readily determined from the direction field for a differential equation.

Two circles c(o, Two circles C(O, r) and C 1 (O 1 , r 1 ) touch each other ...

Two circles C(O, r) and C 1 (O 1 , r 1 ) touch each other at P, externally or internally.  Construction: join OP and O 1 P . Proof : we know that if two circles touch each

Find out the interval of validity, Without solving, find out the interval o...

Without solving, find out the interval of validity for the subsequent initial value problem. (t 2 - 9) y' + 2y = In |20 - 4t|,   y(4) = -3 Solution First, in order to u

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