# Calc I

if f(t)=sqrt(4t+1) find f''(2)

I got the first derivative to be: 1/2(4t-1)^-1/2 * 4t^3

and i'm trying to figure out if i need the product rule again to find the second derivative

-1t^3(4t-1)^-3/2 * 4t^3

The answer if -4/27 and I'm not sure how to get that if I'm doing the second derivative wrong.

1. 👍 0
2. 👎 0
3. 👁 1,339
1. I haven't got a clue how you came up with that first derivative.

f(x) = (4t+1)^(1/2)
f ' (x) = (1/2)(4t+1)^(-1/2) (4)
= 2(4t+1)^(-1/2)

f '' (x) = -1(4t+1)^(-3/2) (4)
= -4(4t+1)^(-3/2)
or
= -4/(√(4t+1)^3 )
f '' (2) = -4/√9^3
= -4/27

1. 👍 0
2. 👎 0

## Similar Questions

1. ### finding c: calc

let f(x)=square root x. if the rate of change of at x=c is twice its rate of change at x=1, then c=? what???? i don't get get it. to begin with, i took the derivative if that helps which is 1/(2*sqrtx) . f'(x) = 1/(2*sqrtx) is

2. ### calculus

Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)

3. ### math-Inverse functions

f(x)=-4x-2 & g(x)=5x-6. Find (f*g) and state domain. f(x)-x^2-1 what is the equation for f^-1(x)? f(x)=3x+2, find f(f^-1(14)). f(x)=4x+7 and g(x)=3x-5 find (f*g)(-4) f(x)=sqrt x+3 what is equation for f^-1(x)? Graph y=sqrt x-2 +5

4. ### calc

find derivative using limit definition: f(x) = x - sqrt(x) so f'(x) = lim h->0 [f(x+h) - f(x)]/h but I keep trying to solve by multiplying by the conjugate but I can't figure it out..there's nothing that can be cancelled or

1. ### algebra

am I right? 1. Simplify radical expression sqrt 50 5 sqrt ^2*** 2 sqrt ^5 5 sqrt ^10 5 2. Simplify the radical expression sqrt 56x^2 28x 2x sqrt 14*** 2x sqrt 7 sqrt 14x2 3. Simplify the radical expression. sqrt 490y^5w^6 2 sqrt

2. ### Calculus

Find the range of y = (3x-1)/(2x^2 + x - 6) I was going to take the derivative of the numerator and denomenator and then use the quotent rule to find the derivative of the function and find the critical values but I ran into the

3. ### Algebra 2

Operations with Complex Numbers Simplify. 1. sqrt(-144) 2. sqrt(-64x^4) 3. sqrt(-13)*sqrt(-26) 4. (-2i)(-6i)(4i) 5. i13 6. i38 7. (5 – 2i) + (4 + 4i) 8. (3 – 4i) – (1 – 4i) 9. (3 + 4i)(3 – 4i) 10. (6 – 2i)(1 + i) 11.

4. ### Math:)

A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates

1. ### increasing and decreasing intervals

Have to find the intervals on which f(x) = 4 - sqrt(x+2) is increasing. Also the intervals on which the function is decreasing. TIA Find the derivative of f(x). When the derivative is positive, the function increases as x

2. ### calculus

find the derivative using quotient rule F(x) = (x - 7 x sqrt(x)) / sqrt(x)

3. ### MATH

For each set of numbers, draw your own number line on a piece of paper, taking care to plot each pair of irrational numbers. Then write a statement comparing the position of the two given numbers on a number line. Also write an

4. ### Calculus

Find the derivative: h(x)=7x/sqrt(5-2x) Using the chain rule...I figured out my previous post.