Let g(x) = 3x - 8. (a) Find the average rate of change from - 5 to 6. (b) Find an equation of the secant line containing (- 5, g(- 5)) and (6, g(6))

Q: Find the slope of the line normal to the graph of y=secx at x=π/4

A:

Q: Find the average rate of change of the function on the interval specified. h(x) = 3 − 6x2  on  [−2,…

A:

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

A:

Q: Find the derivative of the function f(x,y) = x +xy + y at the point (- 2,- 1) in the direction in…

A:

Q: Find the slope and equation of tangent line y=4-x^3, (-1,5)

A: Consider the given equation: y=4-x3 The point where tangent has to be calculated is (-1,5)

Q: Find the derivative of the function f(x.y) = tan -1y at the point (- 9,9) in the direction in which…

A: To find the derivative of a function at a point (-9, 9) in the direction in which the function…

Q: How do you find the derivative using the chain rule?

A: The given equation is hz=ba+z29.

Q: Estimate the instantaneous rate of change of y(x) = 2x² + 2 at the point: In other words, choose…

A: To estimate the instantaneous rate of change of yx=2x2+2 at the point: x=-2.

Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: Find the slope of the tangent line to the curve x² - xy - 2y³ 116 at the point (-2, 4).

A:

Q: Find the average rate of change of f(x)=x² – 5x from: x, =-1 to x, = 3

A: We will find the average rate of change of the function.  We know,  the average rate of change =…

Q: Use the chain rule to find the derivative of f(z) = 4(4z5+5z“) i

A: Given : fx = 44x5+5x4-12

Q: 7. Find the slope of the tangent line at point (-2,2) on the curve f(x) = 2x² + 3x using First…

A:

Q: Find the derivative.

A: Given: To find the derivative of y=2x-3-xx

Q: Find the derivative of the function. 2 + 2

A: To find the derivative of the function, y=rr2+2

Q: What is the slope of the line tangent to the graph of g(x)=1/x at x=1?

A: Given that ,         g(x)=1x          find slope of tangent at x=1

Q: Find the slope of the tangent line drawn to the graph of 2x2−xy−y3=5 at the point (2,1). Enter exact…

A:

Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: Find the slope of the tangent line to the curve y2+x2 = y4-2x at point (-2,1)

A:

Q: Find the equation of the tangent and normal line of the function f(x)=√2x-1 at the point (5,3)

A:

Q: 6. Sketch the graph of y= x2+ by using the properties of the derivative.

A: The given function y=x2+2x

Q: Find the average rate of change of f(x) = 8x2 - x:(a) From 1 to 2       (b) From 0 to 1     (c) From…

A:

Q: 2. What is the slope of the line tangent to the curve 8x3 –- y² = 4 at the point (1,-2)?

A:

Q: The slope of the line through the distinct points (x1, yı) and (x2, Y2) can be interpreted as the…

A: To Determine: the slope of the line through the distinct points can be interpreted as the rate of…

Q: Find the average rate of change of h1x2 = x2 - 2x + 3:(a) From - 1 to 1(b) From 0 to 2(c) From 2 to…

A: Since it is known that the average rate of change can be calculated using the formula…

Q: 3. Tak-gu baked 10 loaves of bread in 1 hour. After that, he baked a dozen of bread in 80 minutes…

A: We have three points,  A = (60 min, 10 )  B = (80 min, 12 )  C = (90 min, 12)    Hence, we have…

Q: Find the slope of the tangent line to the curve x – 4xy + y° = - 23 at the point (- 3, – 2).

A:

Q: Find the slope of the curve y^3+3x^2y-9y=-5 at the point (1,-1) and also find the rate of change…

A:

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: find tangent line to the curve y=3x/7-x at a point of (-3,2/7)

A:

Q: What is the slope of the tangent line to the graph of y-(x-1)/(x+1) at x-1?

A: We have to find

Q: Find the first and second order derivative w=3z7-7z3+21z2

A:

Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

Q: Show that the rate of increase in the slope of the tangent at a point on the curve y = 2x3 is 12…

A: Consider the given curve: Here the objective is to show that the rate of increase in the slope of…

Q: Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on  [−2,…

A: To Find the average rate of change of the function on the interval specified. h(x) = 5 − 6x2  on…

Q: Determine the derivative -d/dv y = 2x³ + 5x - 6 y 1 x² 3x 6x³ + x² − 10x − 3 -

A:

Q: 2. What is the slope of the normal line to the curve 4x2 - 9y2 = 1 at point (3,2) ? a. 3 b. - 8. С.…

A: Normal at any point on the curve is a straight line that intersects the curve at that point and is…

Q: Find the average rate of change and the equation of the secant line for 2x f (x) = from -1 to 3. x²…

A:

Q: Find the slope of tangent line for the equation x^2+y^2=5 on (1,2)

A: The given equation of the line is,

Q: Use implicit differentiation to calculate the value of derivative y' at the solution point (2, y) =…

A:

Q: 2. What is the slope of the line tangent to the curve 8x³ - y² = 4 at the point (1,-2)? 3. What is…

A: In 2 we need to find the slope of the line tangent to the given curve at a point.  in 3 we need to…

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: The slope of the line through the distinct points (x1, y1) and (x2, y2) can be interpreted as the…

A: The slope of the line through the distinct points (x1, y1) and (x2, y2) is defined as…

Q: How do you find the derivative of function y=x^2-2radicalx/x

A:

Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: What is the definition of the derivative (Difference Quotient)?

A: 2. What is the definition of the derivative(difference quotient)? ans. In single-variable calculus,…

Q: What is the average rate of change of f(x)= x2 -2 on the interval [-1,3]?

A:

Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

A:

Exponential Growth Model

The relation that represents an exponential function is: