24) Find the maximum rate of change of at the given point and the direction in which it occurs.

Q: 3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

A: We know, ddxxn=nx(n-1)  , for any real number n. ddxln(x)=1x

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A:

Q: Find a function f so that the maximum rate of change occurs in the direction of u = (1/sqrt(5))…

A: The maximum rate of change occurs at ||grad(f)||. We are given that,       We know that the maximum…

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A:

Q: 2) Find the equation of the curve whose slop 12 B) T= r The rate of change of the temperature, T (in…

A: Step 1: Step 2:

Q: Let f(x, y) = xex²-y and P = (3,9). Calculate || Vfp||. (Express numbers in exact form. Use symbolic…

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Q: 13. A passenger ship and an oil tanker left the port at any time in the morning. The passenger ship…

A: Explanation Given that A passenger ship and an oil tanker left the port any time in the morning  The…

Q: 1) Consider the graph of the function f(x) = 5x -8x a) Find the slope of the secant by sketching a…

A:

Q: If a ball is thrown vertically upward with a velocity of 144 ft/s, then its height after t seconds…

A: Given s = 144 t - 16 t^2 a.Take the derivative with respect to t:ds/dt = 144 - 32 tAt the maximum…

Q: Write the equation for the curve that has slope of 2y/x for each point P(x,y) on it and passes…

A:

Q: Construct a problem where the derivative of a point on a graph is equal to 1. It cannot be a linear…

A: To construct a problem where the derivative of a point on a graph is equal to 1.

Q: The temperature of a potato in an oven is currently 130°F and is increasing by 2.8 degrees per…

A:

Q: Question 10. Find the gradient of the curve f(2) = -2³ + 10z? – 3 at z = 4. Gradient =

A: Let's find.

Q: True or False? The Linear Approximation says that the vertical change in the graph is approximately…

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Q: A cable consists of a core of conductive wire protected by a casing of non-conductive material. Let…

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Q: Find the slope of the curve f(x)= x2 at the point P(2,4)

A:

Q: 3) A researcher has collected population data along with time. Afler comparing the populations from…

A: Solution is given below

Q: y=-sinx . 3π X 2 元 2. 2 N/2

A: Given: y=-sinx

Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: Suppose an arrow is shot upward on a certain planet with an intial height of 1.3 meters and an…

A: