Some interpretations of the derivative, Mathematics

Assignment Help:

Some interpretations of the derivative

Example   Is f ( x ) = 2 x3 + 300 +4 increasing, decreasing or not changing at x = -2 ?

Solution:  We already know that the rate of change of a function is specified by the functions derivative so all we have to do is it rewrite the function (to deal along with the second term) and then take the derivative.

f ( x ) = 2 x3 + 300 x-3+4       ⇒       f ′ ( x ) = 6x2 - 900x-4  = 6x2 - 900/x4

Note as well that we rewrote the last term in the derivative back as fraction. It is not something we've done to this point & it is only being done here to help with the evaluation in the next step. It's frequently easier to do the evaluation with +ve exponents.

Hence, upon evaluating derivative we get

f ′ ( -2) = 6 ( 4) - 900/16 = - 129/4 = -32.25

Hence, at x = -2 the derivative is negative and therefore the function is decreasing at x = -2 .

 


Related Discussions:- Some interpretations of the derivative

Tests for relative minimum, Tests for relative minimum For a relative ...

Tests for relative minimum For a relative minimum point there are two tests: i.The first derivative, which is (dy)/(dx)  = f´(x) = 0 ii.The second derivative, which i

Without a calculator give the exact value, without a calculator give the ex...

without a calculator give the exact value of each of the following logarithms. (a) (b) log1000 (c) log 16 16 (d) log 23 1  (e)  Solution (b) log10

Multiplication of binomials, To understand the multiplication of binomials,...

To understand the multiplication of binomials, we should know what is meant by Distributive Law of Multiplication. Suppose that we are to multiply (a + b) and m. We

Geometry, all basic knowledge related to geometry

all basic knowledge related to geometry

Math on a spot, compare: 643,251: 633,512: 633,893. The answer is 633,512.

compare: 643,251: 633,512: 633,893. The answer is 633,512.

Examples of linear equation, Examples of Linear Equation Please provid...

Examples of Linear Equation Please provide me some Examples of Linear Equation?

Making connections with maths, MAKING CONNECTIONS :  you have read about w...

MAKING CONNECTIONS :  you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo

Explain the rules of divisibility, Explain the rules of Divisibility ? ...

Explain the rules of Divisibility ? Divisible by 2: If the last digit is a 0, 2, 4, 6, or 8, the number is evenly divisible by 2. Divisible by 2 Not

Sums, what is 10 times 10 pls

what is 10 times 10 pls

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