Wednesday

August 27, 2014

August 27, 2014

Posted by **hy** on Monday, October 25, 2010 at 12:03am.

(k is constant) X^2, x > and equal to 1

A) find value of k such that h(x) is continous at x=1

B) determine if h(x) is differentiable at x=1

- calculus -
**MathMate**, Monday, October 25, 2010 at 8:47ama)

For h(x) to be continuous,

we need to address the point x=1, since the rest are continuous.

h(x)=x² for x≥1 means that

h(1)=1²=1

We therefore require that

lim h(x) x->1- = 1, or

set h(x)=kx+1 = 1 => k=0

Therefore h(x)=0*x+1 =1

b) h'(1-) = d(1)/dx =0

h'(1)=h'(1+)=d(x²)/dx = 2x = 2

Since h'(1-)≠h'(1+), we conclude that h(x) is not differentiable at x=1.

**Related Questions**

calculus - Determine the exact value for the constant k such that the area of ...

Calculus - consider k(t)=(e^t)/(e^t-7) on[-7,7] Is this function continuous on ...

calculus - LEt f and g be continous functions with the following properties i. ...

calculus - LEt f and g be continous functions with the following properties i. ...

Calculus Quiz Today - 1. find the values of s for which each function is ...

calculus - Let f be defined as follows: h(x)= -x-3 for x greater than or equal ...

calculus - Consider the function f(x)=65x−cos(x)+2 on the interval 0 less ...

math,help - I definately do not understand this problem. If y varies directly ...

Calculus - Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than...

Calculus - sketch the graph of a function f that is continous everywhere except ...