.  (a) Sketch the graph of y = 2x2 over the interval [-1,1] (b) Let x be any point in the interval [-1,1] and let A(x) denote the area under the graph over the interval [-1,x]. It follows that A′(x) = 2x2. Find an expression including an arbitrary constant for A(x) (i.e. find a func- tion whose derivative is 2x2). Verify that the derivative of your expression gives A′(x) = 2x2. (c) Find the value of c in your expression by considering A(x), the area under the graph over [-1,x], when x = −1.

Q: 6) Differentiate: a) f(x)= 5x-3 +1)

A:

Q: Horizontal asymetote6) Domainoin Interual notalion!

A:

Q: A ball is thrown from the top of a wall onto horizontal ground. The path of the ball is modelled…

A: The path of the ball is given by the below function. fx=6+8x−x2 To determine the height from which…

Q: Find the point on f(x) 1 4 = )` √ that has a slope of

A: As we know the slope of the tangent line to the given curve is equal to the derivative of the given…

Q: given that f(x) =x-1, and g(x) =2x2 -1, determine (g (dot product) f)(x)     i put "(dot…

A: The given function is: f(x)=x-1           and             g(x)=2x2-1

Q: Find x- and y-intercepts for f(x)=(x+2)2(x-1)

A: Topic- function

Q: By carefully showing all your steps, differentiate the function f(x) = (tan−¹(x + √√x)) 4

A:

Q: Make the composition (f o g) (x) with the function f (x) = x ^ 2 + 2 -2 and g (x) = √x

A: