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- Let g(x)= arctan(x^3 + 3x^2 - 9x). Find where g(x) is increasing. I know the values of x which g(x) has a hortizontal tangent are x +-3 and x = 1, but I don't know of I should just graph it or use those to find where it increases.Find the values of h, k, and a that make the circle (x - h)2 + (y - k)2 = a2 tangent to the parabola y = x2 + 1 at the point (1, 2) and that also make the second derivatives d2y/dx2 have the same value on both curves there. Circles like this one that are tangent to a curve and have the same second derivative as the curve at the point of tangency are called osculating circles.Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini Let f ( x ) = x^2 + 5 x + 10 (a) When is the rate of change of f(x) zero? x = (b) On what interval is the derivative positive? (Use I for infinity and -I for negative infinity.) < x < (c) On what interval does the graph y = f ( x ) have positive slope? (Use I for infinity and
- Given the function in the image provided answer the following: A) Is the function continuous if x=1? B) Show that f’(1) doesn’t exist C) Is there a tangent line to the function at P(1,f(1)) ? I will attach a photo of the whole exercise just so you can see what I mean by f’ and P is point Thef(x) = 10 cos x + 5 sin 2x Determine the points in the interval (0, 2π) at which the graph of the function below has a horizontal tangent line. -there should be 3 (x , y) values from smallest to largest x valuea) Find the point on the graph of y = sinh x at which the tangent line is parallel to the line through (1, 2) and (2, 4). b)Find the points of inflection and comment on concavity for the graph y = x sin-1 x. c) An outdoor thermometer registers a temperature of 40◦F. Five minutes after it is brought into a roomwhere the temperature is 70◦F, the thermometer registers 60◦F. When will it register 65◦F ? same questions are in iamge as well
- a. Find the local extrema of each function on the given interval,and say where they occur.b. Graph the function and its derivative together. Comment onthe behavior of ƒ in relation to the signs and values of ƒ′.59. ƒ(x) = sin x-cosx, 0 ≤ x ≤2ΠGraph f (x)/g(x) and f ′(x)/g′(x) near x = 0. What do you notice about these ratios as x 0? How does this illustrate L’Hôpital’s Rule? f(x) = sin 3x, g(x) = sin 4xa. Find the local extrema of each function on the given interval,and say where they occur.b. Graph the function and its derivative together. Comment onthe behavior of ƒ in relation to the signs and values of ƒ′.59. ƒ(x) = sin x+sqrrt(3)cosx, 0 ≤ x ≤2Π
- Find the points of inflection and discuss the concavity of the graph of the function. f(x) = sin x + cos x, [0, 2 ]The curve x^3+y^3−3xy=0 is known as the Folium of Decsartes. In 1638 the famous philosopher, diplomat, soldier and mathematician René Descartes challenged the lawyer and rival mathematician Pierre de Fermat to find the tangent to this curve at an arbitrary point. Fermat easily found the tangent, which is quite impressive since his method pre-dates Calculus by about 40 years! Now, about 400 years later we can find the tangent easily using implicit differentiation: dydx= . Evaluated at the point [a,b]=[2/3,4/3]=[2/3,4/3] the gradient is m=dydx(2/3,4/3)(2/3,4/3)= . The formula for the equation of the tangent at [a,b] with gradient m is: y−b=m(x−a) At the point [a,b]=[2/3,4/3]=[2/3,4/3], this can be rewritten as y== . The Folium of Descartes (red) and the tangent at [2/3,4/3][2/3,4/3] (blue) are displayed belowFind the points of inflection and discuss the concavity of the graph of the function. f(x) = sin x/2, [0, 4 ]