Friday

November 28, 2014

November 28, 2014

Posted by **Vanessa** on Friday, January 4, 2013 at 11:04am.

A. Find the values of a a b such that g(x) is a differentiable function.

B. Write the equation of the tangent line to g(x) at x = 2pi.

C. Use the tangent line equation from part B to write an approximation for the value of g(6). Do not simplify.

- calculus -
**Steve**, Friday, January 4, 2013 at 11:37amsince each part of g is differentiable, we need the slopes to match up at x=2π, so that dg/dx is defined everywhere.

dg/dx =

a cos x for x <= 2π

2x-π for x > 2π

so, we need

a cos(2π) = 2(2π)-π

a = 3π

g(x) is thus

3π sinx + b

x^2 - πx + 2

and we need g to be continuous, so needs must

3π*0 + b = (2π)^2 - π(2π) + 2

b = 2π^2 + 2

g(x) =

3π sinx + 2π^2 + 2

x^2 - πx + 2

g(2π) = 2π^2+2

g'(2π) = 3π

so we want the line through (2π,2π^2+2) with slope 3π:

y-(2π^2+2) = 3π(x-2π)

when x=6,

y-(2π^2+2) = 3π(6-2π)

y = 18π-6π^2 + 2π^2+2

= 18π-4π^2+2 = 19.070

In fact, g(6) = 3π sin(6) + 2π^2 + 2 = 19.106

**Answer this Question**

**Related Questions**

calc - i did this problem and it isn't working out, so i think i'm either making...

Calculus - Find the interval(s) where the function is increasing where and it is...

Calculus - Consider the function f(x)=sin(1/x) Find a sequence of x-values that ...

Calculus - Consider the function f(x)=sin(1/x) Find a sequence of x-values that ...

Maths - Eq of curve is y=b sin^2(pi.x/a). Find mean value for part of curve ...

math - Solve the following equations giving any roots in terms of pi in the...

math-PLEASE CHECK - Find the surface area and volume of each of the following ...

math - Evaluate. 1. sin^-1(-1/2) 2. cos^-1[(-root 3)/2] 3. arctan[(root3)/3] 4...

Precalculus with Trigonometry - What values of theta between 0 and 2pi solve the...

Calculus - Consider the curve defined by y + cosy = x +1 for 0 =< y =< 2pi...