Let f(x)= 2x° + 3x 2 - 12x- 3. a. Find all points on the graph b. Find all points on the graph a. The tangent line is horizonta nair Ise

Q: Find an equation of the line tangent to the graph of f at the given point. f1x2 = sin-1 12, p>62 4

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Q: Let f(x) = 14x + 11 – 3e. Then the equation of the tangent line to the graph of f() at the point (0,…

A: Given: f(x)=14x+11−3ex The equation of the tangent to the graph f(x) at the point (0,8), is given…

Q: Given that f(7) = 1 and f'(7) = -7, find an equation for the tangent line to the graph of y = f(x)…

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Q: (a) If g(x) = x2/3, show that g'(0) does not exist.(b) If a ≠ o, find g'(a).(c) Show that y = x2/3,…

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Q: Find all values of x for which the tangent line of f(x) = /x² + 18x+96 is horizontal. A 0,-9 B 0,9 С…

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Q: a. Determine the point (a, la)) for which f'(a) = a, given that Ax) = -x + 3x-7. b. Write the…

A: For (a), Given: We need to find the point a for which f'(a)=a. Here, f'(x)=-2x+3. So,…

Q: Let f(x) = 12x + 11 – 15e*. Then the equation of the tangent line to the graph of f(x) at the point…

A: Solving by equation of tangent we have

Q: Find all values of the parameter pp for which the line y=2x+1 is tangent to the graph of y=px2+3.…

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Q: Given that f(2) =-7 and f'(2) = -8, find an equation for the tangent line to the graph of y = f(x)…

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Q: Let y = 5 -5 and x = t – e'. Find any points which have a horizontal or vertical tangent line.

A: The parametric curve has a horizontal tangent if dydt=0;dxdt≠0 and vertical tangent if dxdt=0;dydt≠0

Q: Let g(x) = x 3. Calculate g'(a), and explain why g' does not exist when a = = 0. Sketch a graph of y…

A: Consider the function: gx=x23g'x=ddxx23Apply the Power Rule:   ddxxa=a⋅xa−1…

Q: Let f(x) = 2x + 5 – 5e". Then the equation of the tangent line to the graph of f(x) at the point (0,…

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Q: The graph of ax + b f(x) = (æ – 1)² has a horizontal tangent line at (–3, –). Find a and b.

A: For horizontal tangent line at a point derivative of the given curve is zero , just used it and…

Q: 98. Find the points on the graph of y = 2x6 – x* - 2 at which the tangent line is horizontal.

A: Find the points on the graph of  y=2x6-x4-2at which the tangent line is horizontal.

Q: find (a) the slopeof the curve at the given point P, and (b) an equation of the tangentline at P. y…

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Q: The graph of 3 (x+y) = 25 (x -y²), shown in the figure, is a lemniscate of Bernoulli. Find the…

A: Given query is to find equation ifbthe tangent at given point.

Q: Consider the graph of f (x) = 16 – x². f(x) P Find the coordinates of the point P in the graph at…

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Q: Given that f(4) = -8 and f'(4) = –6 , find an equation for the tangent line to the graph of y = f(x)…

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Q: Let f(x) = 14x + 6 - 17e. Then the equation of the tangent line to the graph of f(x) at the point…

A: The given function is fx=14x+6-17ex we have to find the equation of the tangent line at the point…

Q: Let f(x) = 8x + 14 – 19e*. Then the equation of the tangent line to the graph of f(x) at the point…

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Q: If g(x) = 2 − x3, find g'(0) and use it to find an equation of the tangent line to the curve y = 2 −…

A: g(x)=2-x3differentiate w.r.t xg'(x)=-3x2Put x=0g'(0)=-3(0)2 g'(0)=0at x=0g(0)=2-02⇒y=2.equation of…

Q: Let f(x) = 4x + 7 – 17e². Then the equation of the tangent line to the graph of f (0, -10) is given…

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Q: Find values of a, b, and c such that the graph of f(x) = ax³ + bx² + cx_has a horizontal tangent at…

A: The graph passes through (1,1). So at x=1, f(x)=1

Q: Trace the curve r² = 4cos*etan?o.

A: The given curve is r2=4cos4θtan2θ. Simplify as follows:…

Q: (a) If g(x) = x2/3, show that g'(0) does not exist.(b) If a ≠ 0, find g'(a).(c) Show that y = x2/3…

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Q: Suppose that f is a function given as f(x) = x° + bx? + cx – 2. Find the exact values of b and c if…

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Q: Let f(x) = 4x + 5 – 19e“. Then the equation of the tangent line to the graph of f(x) at the point…

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Q: Given the function f(x)=−2xcos(x), find f′(x). Then find the equation of the tangent line at at the…

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Q: If G(x) = 4x² – x³ find G' (a) and use it to find equations of the tangent lines to the curve y =…

A: Given, y = 4x2 - x3 Differentiating y with respect to x  we will get slope of tangent to the curve…

Q: Given that f(−6)=−6 and f′(−6)=−6, find an equation for the tangent line to the graph of y=f(x) at…

A: We know that slope of tangent line to the graph of y=f(x) at x=a is f'(a) Therefore, slope of…

Q: If g(x) = 5 – x³, find g'(0) and use it to find an equation of the tangent line to the curve y = 5 –…

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

Q: The graph of y=a3x2+a2​, where a is a constant is called the witch of Agnesi.   a. Let a=6 and find…

A: a). Given, y=216x2+36 Differentiating with respect to x, we get…

Q: (a) If g(x) =x2/3 , show that  g'(0) does not exist.(b) If a≠ 0 , find g'(a) .(c) Show that y= x2/3…

A: Given function is gx=x23. Differentiating the function with respect to x,…

Q: Consider the graph of f(x) = 11-x^2. Find the coordinates of the point P in the graph at which the…

A: Let the tangent passes through (h,k) (h,k) is on f(x) = 11-x2. So k=11-h2 That means (h,k)=(h,…

Q: If a is a positive integer, then the slope of the tangent to the graph of y = a? + In(az + 1) at a =…

A: To find the slope of the tangent to the graph of the given equation

Q: Which of the following is/are points on the curve y = x4- 8x3 + 22x2 - 24x + 9 where the tangent…

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Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = −1 and B ′(24) =…

A: Given thaty=B24 x=24y=B24 =-1B'24 =-14To :find equation of tangent line Solution :equation of line…

Q: Sketch a graph of y? = x* – 12x , find the coordinates of the points on the graph of y? = x³ – 12x…

A: giveny2=x3-12xwhen tangent line is Horizontal ,then slope will be zero.differentiate the…

Q: For what value(s) of x does the graph of 1 f(x) = – x² +3 have a .2 - horizontal tangent?

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Q: For the curve f(x) = 1+40x^3-3x^5 , what is the point of inflection (maximum) of the tanent line…

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Q: Let f(æ) = 12a + 3 - 17e". Then the equation of the tangent line to the graph of f(x) at the point…

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Q: Let f(x) = 2x + 15 – 7e". Then the equation of the tangent line to the graph of f(x) at the point…

A: We know that equations of tangent line at the point (x1,y1) is given as - ( y - y1 ) = m ( x - x1 ).…

Q: At which point(s) does the graph of  y= e((x3-2x2+3x)/(x)) have a horizontal tangent line?

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Q: If f(2) = 6, and f'(2) =-1.2, find the coordinates of points A, B, and C. Line segment BC is tangent…

A: Given that f(2)=6 , that means A=(2,6) Given that f'(2)=-1.2 So the slope of the tangent is -1.2 and…

Q: Let f(x) = 6x + 9 – 17e". Then the equation of the tangent line to the graph of f(x) at the point…

A: A tangent is a line which just touches a curve and in some sense is parallel to the curve. The slope…

Q: Choose the correct graph of y = sin x, -"sxS T: 1 -37 21 -1 -2

A: The given function is: y=sin x ;                 -3π2≤x≤π

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 24 if B(24) = 0 and B'(24) = -…

A: Given,         y=Bx at x=24 if B24=0 and B'24=-14.

Q: Choose the correct graph of y = sin x, - T < x < 2 T; and y = csc x, - T < X< 2T: 2 1 27 -1 -2

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