A function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where a, b and c are real numbers. It is given that the tangent plane to the graph of f at the point (-1, 3, f(−1, 3)) has equation z =-6x-y-3. a) Explain why the information given tells you that f(-1,3) = 0. b) Consider the contour line of the function f through the point (-1, 3) in the (x, y)-plane. Find the equation of the tangent line to this contour line at the point (-1, 3). You do not need to find the values for a, b and c to answer this question! c) Find the values for the numbers a, b and c.

Q: Suppose that f(2) = 2. f'(2) = 8, g(2) = 2, and g'(2) = -2. If F(x) = (f • g)(x) and G(x) = (g •…

A:

Q: 1) BASIC DERIVATIVES: Differentiate and simplify the following functions a) f(x) = 5x³+3x² - 5x+2 b)…

A: We know that the derivative of x^n Is  nx^(n-1)

Q: Find the points on the graph where the tangent line to the curve (x2 + y²)² = 10 (x² – y²) + 8 is…

A: The given curve is, x2+y22=10x2-y2+8 The graph of this curve is as follows,

Q: Derivative of y = 16 is: a) 1 b) 0 Derivative of f(x) = - 6x + 2 is: a) - 4 b) 2 Derivative of g(x)…

A:

Q: What is the slope of the secant line that passes through the points(a, f(a)) and (b, f(b)) on the…

A: Given: The secant line passes through the points a,fa  and  b,fb. Concept used: The slope of a line…

Q: Part 1 a) Given f (z) = + x2 + i(2x2 - y?), show which points where f has y a derivative. b) Show…

A:

Q: d) increasing decreasing. (You may use maple. However, you must clearly show how you used the first…

A: Given that fx=x4+x3-2x2+2x2+x-2

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: Bonus) Find the equation of the secant line that passes through f(x) = -(x + 2)² at (2, f(2)) and…

A:

Q: 4. Which graphs of ƒ may have a point of inflection? State the coordinates of each point a) ƒ''(-4)…

A: For a function f, if its second derivative f″(x) exists at x0 and x0 is an inflection point for f,…

Q: Sketch a function where ?′(?) > 0  and ?′′(?) > 0 always and passes through the point (0,1).

A:

Q: Plot the graphs of f(x) = x(x - 3) (x + 3) and g(x) = cos 2 x together on the same set of axes and…

A: In the question it is asked to draw diagram for f(x)=x(x-3)(x+3). Also it is asked to draw…

Q: A baseball is hit at a point 3 feet above the ground at a velocity of 100 feet per second and at an…

A: The main objective is to find the axis of symmetry of f(x) and maximum height ball reaches.

Q: The equation of the line tangent to the differentiable and invertible function f(x) at the point (5,…

A:

Q: Write an equation of the tangent line to the graph of y = f(x) at the point on the graph where x has…

A: To write an equation of the tangent line to the graph of, y=fx, at the point on the graph where x…