# What is the slope of #f(t) = ((t-2)^3,2t)# at #t =-1#?

Slope at

By signing up, you agree to our Terms of Service and Privacy Policy

To find the slope of ( f(t) = ((t-2)^3, 2t) ) at ( t = -1 ), we first need to find the derivative of ( f(t) ) with respect to ( t ), then evaluate it at ( t = -1 ).

The derivative of ( f(t) ) with respect to ( t ) is given by:

( f'(t) = \left( \frac{d}{dt}((t-2)^3), \frac{d}{dt}(2t) \right) )

( = \left( 3(t-2)^2, 2 \right) )

Now, evaluate ( f'(t) ) at ( t = -1 ):

( f'(-1) = \left( 3((-1)-2)^2, 2 \right) )

( = \left( 3(-3)^2, 2 \right) )

( = \left( 3(9), 2 \right) )

( = \left( 27, 2 \right) )

Therefore, the slope of ( f(t) ) at ( t = -1 ) is ( 27 ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the derivative of #f(t) = (t^3-e^(3t-1) , t^2+te^t ) #?
- How do you differentiate the following parametric equation: # x(t)=-te^t+t, y(t)= 3t^3-4t #?
- For #f(t)= (sint-cost,t)# what is the distance between #f(pi/4)# and #f(pi)#?
- How do you find parametric equations for the tangent line to the curve with the given parametric equations #x=7t^2-4# and #y=7t^2+4# and #z=6t+5# and (3,11,11)?
- What is the arclength of #(sqrtt,1/sqrt(t^2+3))# on #t in [1,2]#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7