Find the equation of the tangent line to the function y = − x² + 7 at the point (-1,6). No decimal values! What is the derivative of y? The equation of the tangent line in y = mx + b form:

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A: Given:    fx=-2x2 when x=-2     f-2=-2-22               =-8 when x=0     f0=-20=0 when x=1…

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A: Please see the below picture for detailed solution.

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Q: Find the complex zeros of the quadratic function. Graph the function and label the intercepts. f(x)…

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Q: The figure below is the graph of a second derivative f". What are the x-values that are inflection…

A: Given the graph of a second order derivative

Q: Express the given quantity as a single logarithm. =1/12 In((x + 2)9) + [in(x) - In((x² + 3x + 2)²)]…

A: f(x)=19ln(x+2)2+12lnx-ln(x2+3x+2)2we know lnxn=nlnxlnab=lna-lnb

Q: 5) Here is a description of the derivatives of f: f'(-1) DNE, f'(2)=0 f'(x)>0 when x2 f'(x)0 when 15…

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Q: 5) x² √2x - x² S√zi

A: ∫x22x-x2dx since you have posted multiple question i can answer first question as per our company…

Q: line to the graph of y = g(x) at x = 4 is 4x+12y = -56 It follows that y = is the equation of the…

A: Given that at x=4, 4x+12y=-56 is a tangent.

Q: 2) Here is a derivative chart for f(x) f" + + DNE DNE + 1 O 7 + O S -2 a) Sketch the graph of f(x)…

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Q: 41. Calculate 3 f(x) dx, where -2 f(x) = { 12-x² for x ≤ 2 for x > 2 +3

A: Integration

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A: Given: The hands of the clock are approximately 4.5 m and 2 m in length, that is, the minute hand is…

Q: Solve equation (10) from Section 7.4 + ["i(t) dr = E(t) (10) L+Ri(t) + dt subject to i(0) = 0 with…

A: The given differential equation is: Ldidt+Ri(t)+1C∫0t i(τ) dτ=E(t)

Q: Find the solution of the following initial value problem. = 9x (x² - 1); g'(x) = 9x xo The solution…

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Q: H 1 in 1in 1 in 3 in 1 in

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Q: √√3 9. ² 2 0 4x² (1-x²)z dx

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: Given: Half-life of radium = 1590 years To find: Time taken to disappear 1/6 of the radium. Formula…

Q: Hoziontal and Vertical Components Find the horizontal, x, and vertical component, y, of each vector…

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Q: ) It is given to you that an equation of the tangent line to the graph of y = g(x) at X = 16 is…

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Q: 1 The price p (in dollars) and the quantity x sold of a certain product obey the demand equation p =…

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Q: ax Find the value of a so that the function f(x) = xex has a critical point at x = = 3.

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Q: During Appreciation Day, a school bought some roses and cookies for their parents volunteers. The…

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Q: Graph the function. Then use the derivative and algebra to find the location of the critical points…

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Q: Determine if f is continuous at all possible points of discontinuity. Classify each discontinuity as…

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Q: Problem #5: Evaluate the following, 343 (x² + 2) e-7x dx, and write your answer in the form g(x)…

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A: We are to show  how to approximate the required work by a Riemannsum. Then express the work as an…

Q: Find the dimensions of a rectangle with a perimeter of 160 ft that has the largest possible area.…

A: We know formula for rectanglePerimeter of a rectangle=2l+bArea of a rectangle=length×breadthGiven:…

Q: Consider the following position function. Find (a) the velocity and the speed of the object and (b)…

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Q: (a) Find all the x-values of the critical points and inflection points of the function f(x) = x¹ −…

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Q: Use the first derivative and the second derivative test to determine where each function is…

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Q: shift of the graph as described in the lesson, what values of m and n will make the graph of…

A: We will find the required.

Q: Find the slope of the tangent line to the ellip x² y² + 25 4 slope = = 1 at the point (x, y).

A: given ellipse equation is :-x225+y24=1  then we have to find slope  of the tangent  line to ellipse…

Q: Linear DE of order One the steps are in the picture solve the following differential equation…

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Q: For the following vector field, compute (a) the circulation on and (b) the outward flux across the…

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Q: The graph of y = f(x) (solid) and its tangent line at (-3,-4) (dashed) is shown. 10 9 8 7 6 5…

A: Given graph of a function f(x) and it's tangent at x=-3

Q: (x + 4)² dx

A: 42. The given integral ∫x+42dx. We have to find the integral.

Q: Given an acceleration vector, initial velocity (uo,vo), and initial position (xo.Yo), find the…

A: Here we have to find the velocity vector.

Q: f(x) = -4 f(x) = 2 f(x) = ∞ f(x) = -∞ Che following might be a graph of y = f(x)? 2. -7 -6 -5 -4 -3…

A: we will find the required.

Q: Diana has available 520 yards of fencing and wishes to enclose a rectangular area. (a) Express the…

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Q: An employee's monthly productivity M, in number of units produced, found to be a function of the…

A: Given query is to find the year when maximum productivity achieved.

Q: Consider f(x) = (a) f'(x)= = x² -1x - 78 x+6 (b) Find all points P(x, y) on the curve y = f(x) whose…

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Q: Consider the graph of Cx + Ay = B where A, B, and C are all positive consta (a) Find the coordinates…

A: Given: Cx+Ay=B

Q: 5) Differentiate f(x) = √3x² + 4x.

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Q: I'm confused on how you got 1.905 in the numerator

A: Pi = 3.14    The rate of volume of gravel dumped is: dv/dt = 10 In circular cone relation between…

Q: Find dy/dx by implicit differentiation. xey = x - y y' =

A: Note : according to our guidelines i can solve only first question please reroute the remaining one.…