Suppose f"(x) = (x + 2)°(x + 1)²(x – 2). Which of the following statements about the curv y = f(x) is true? O The curve is concave up on the intervals (-o,-2) and (2, o) and concave down on the intervals (-2, -1) and (-1,2). O The curve is concave down on the intervals (-0, -2) and (-1, 2) and concave up on the intervals (-2, -1) and (2, co0). O The curve is concave down on the intervals (-00, -2) and (2, 0) and concave up on the intervals (-2, -1) and (-1,2). O The curve is concave up on the intervals (-o, -2) and (-1,2) and concave down on the intervals (-2,-1) and (2, 00).

Q: Determine the slope of the tangent to √1-x at the point (-8, 3).

A:

Q: Find the derivative the following functions. a) h(x) = 4√√x+3x8 +5ex + π² x³-6x²+8x b) g(x) x²-2x =

A: The given functions are The aim is to find the derivative of the given functions.

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: Create a 3-D plot of the function sin(/x² + y²) Vx² + y² for -8 <x5 8 and –8 < x < 8.

A: Note: Here, we are considering -8 ≤ x ≤ 8 and -8 ≤ y ≤ 8 rather than -8 ≤ x ≤ 8 and -8 ≤ x ≤ 8. We…

Q: For a function g, we are given that g(-6) = -8 and g'(-6) = 3. What's the equation of the tangent…

A: For a function , we are given that  and .To find the equation of the tangent line to the graph of…

Q: (6) Let a be a positive real number. Consider the curve defined by r? + y² – ry = a². Find all…

A: Given curve is x2+y2−xy=a2. Differentiate x2+y2−xy=a2 with respect to x, we get…

Q: 9. Find the slope of f(x) = (x+2)2 +5 at the point (3,-4)

A:

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: