y-y=m(x-x,S (0, -1) arnd slope m = -2

Q: Find the equation of the tangent and normal line of the function y^3 +3xy + x^4 = 5 at the point (1,…

A: y3+3xy+x4=5 Differentiating with respect to x, we get…

Q: 3. The slope of tangent line at any point (x, y) on the curve is 3x²-2x+7. What is the equation of…

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Q: Find the curve y = f(x) in the xy-plane that has the given properties. f(x) has a slope at each…

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Q: 2x +1 Find the slope of the line tangent to the graph of y = 5x at x = 1. 4

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Q: A. Find the slope of the curve y=x2-2x-3 at the point P(2,-3) by finding the limiting value of the…

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Q: At what point(s) on the curve  x = 6t2 + 6, y = t3 − 4  does the tangent line have slope  1 2? (x,…

A: Find the slope which is the tangent then follow the steps shown below.

Q: a. Find the slope of the curve y = x - 2 at the point P(-1,-3) by finding the limiting value of the…

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Q: Q3) Determine slope of a curve y = x + 2 at p(1,3) and q(3,11)

A: Slope of a curve : The slope of a curve y=f(x) at a point P is the slope of the tangent at that…

Q: The curve y = ax² + bx + c passes through the point (1,8) and is tangent to the line y= 6x at the…

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Q: 18,8grt(10)) 10 f(x) = V2x – 2 compute the instantaneous slope at: (6, v10) Start with two points A:…

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Q: The slope of the tangent line to the curve y = f(x) is perpendicular to the line 3x-2y =5. The slope…

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Q: Differentiate implicitly to find Then find the slope of the curve at the given point. x²y - 3x - 4 =…

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Q: tangent line

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Q: f(x) = 4x^2 - 4x^3 + 4 What is the slope of the tangent line at x=2?   What is the equation of the…

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Q: The curve for which y'' = 6 has a slope of –3 at its point of inflection (2, 3). Find the value of y…

A: y''' = 6 Implies, y" = 6x + a, where, a is a constant. &, y' = 3x² + ax + b, where, b is a…

Q: 8. For g(x) =x +1, i] find the average rate of change from -1 to 2. ii] find the equation of the…

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Q: h(x) = x2 - 2x(a) Find the average rate of change from 2 to 4.(b) Find an equation of the secant…

A: Given function is hx=x2-2x. To find: (a). The average rate of change from 2 to 4. (b). Equation of…

Q: Find all points (x,y) on the graph of f(x) = 2x- 3x with tangent lines parallel to the line y= 13x +…

A: Given : f(x) = 2x2 - 3x     To find the points on the graph of f(x) = 2x2 - 3x with tangent lines…

Q: 2x +5 at x = The equation of the line tangent to f(x) x - 2 y = 9x +

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Q: The curve for which y'' = 6 has a slope of –3 at its point of inflection (2, 3). Find the value of…

A: Given that, y'''=6

Q: Find the equation of the curve that passes through the point (0, 3) and has a slope of 2 x+1 O y =…

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Q: with a slope of 2. 48. Find the equation of the tangent and normal lines to the curve y x+x² – x+1…

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Q: 0. Find the length of the curve y = x/2 + 8 on the interval (0, 2]

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Q: 20. What is the instantaneous slope of y at x = 2? %3D -1 1 112

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Q: Q2: Find all relative extrema and saddle point of f(x,y) = 3xy +y-x' +3

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Q: a. For f(x) =-, find an equation for the secant line through the points where x = 1 and x= 5. b. For…

A: Given data -  f(x) = 5/x we have to find - a. An equation for the secant line through the point…

Q: Find the point at which the line y = 8x – 31 is tangent to the graph of y = eXf-16). %3D The point…

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Q: find the slope of the curve y=x^2-4x-4 at the point P(3,-7) by finding the limiting value of the…

A: Now let the secant line passes through the points  Now slope of the secant line is,

Q: 2x+1 Aliza says that there is no tangent line with a negative slope for the f(x)% = Stella disagre…

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Q: etermine the equation of the tangent line to the graph of f(x) = O y = 6 + 6x y=-6x - 6 Oy=6-6x x

A: Topic:- application of derivatives and integration

Q: What is the slope of the tangent line to the graph of y= x*-3x2 + x +2 at x-17 [a) What is the…

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Q: Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at the point P(5, 0). 1. max slope 20T 2.…

A: Given:- f(x, y) = 4 sin(xy) To find:- Find the maximum slope on the graph of f(x, y) = 4 sin(xy) at…

Q: Find a point on the graph of 3x y = x-4 12 where the slope of the tangent is - 23. (find x value…

A: This question can be solved using the concept of slope of tangent at a given point.

Q: 19. For what values of the constants a and b is (1, 3) a point of inflection of the curve y = ax³ +…

A: Consider the value of y and solve:

Q: The slope of the tangent line to the curve y - f(x) is perpendicular to the line3x-2y -S . The slope…

A: topic - slope of perpendicular line

Q: The curve y = f(x) has a y – intercept of 3. The tangent to this curve at the point (x, y) has an x…

A: Given that the curve y=f(x) has a y-intercept of 3.  That means y(0)=3. also given that the tangent…

Q: Find the slope of the curve x^3=(y-x^2)^2 at (1,2). If q-p=Inq+Inp, find dq/dp.

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Q: A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of…

A: A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of…

Q: The curve for which y" = 6 has a slope of -3 at its point %3| of inflection (2, 3). Find the value…

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Q: The x value(s) of the point(s) where the tangent lines) to the curve y = 1/3x3- 6x that have a slope…

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Q: 6. Consider the curve 5x - xy + y =7. The slope of the line tangent to the curve at the point (1,2)…

A: To find the slope of the line tangent at the point (1,2) is substituting the point in the dy/dx . We…

Q: C(x) = 1500 + 13x – 0.1x2 + 0.0005x3. - %3D Find the marginal inal cost finctien?

A: Given query is to find the marginal cost function.

Q: e-Sx at the point where x = 0. Find an equation of the line tangent to the graph of y = x³+1

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Q: The cubic function y = ax3 + bx2 + cx +d pass through (0, -6), (1, -2) and tangent to the line 3x -…

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Q: Maria thinks that the maximum point of y= -(z – 1)* + 1 is (0, 1), Jena disagrees. Who is CORRECT?…

A: Maria thinks that the maximum point of y=-(x-1)2+1 is (0, 1)

Q: Bonus: Find the equation of the line tangent to f (x) = 3x – e-5x when x = 0.

A: Given: fx=3x-e-5x To Find: Equation of the line tangent to fx, when x=0. Concept: Equation of Line…

Q: p) Find the equation of the line tangent to the curve x² + y² = 25 at (3,4) %3D

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Q: A curve for which y" = x passes through the point (1, –1) with a slope of. Find the y-value of at x…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q4) Find the equation of the normal to the curve [y+x(1+y)-4] at point (2,1).

A: Given equation is y2+x1+y-4=0 and we have to find the equation of normal to the…