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- Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.Find the point (x0,y0) on the graph y=x^3 + 6x^2 +3x -5 at which the slope of the tangent line has its minimum value (enter your answer as a coordinate point in the form (* , *) (x0,y0) = _____________________a. Find the function f given that the slope of the tangent line to the graph of f at any point (x,f(x)) is xe-2x and that the graph passes through the point (0,3). b. In keeping with the projected increase in worldwide demand for steam coal, the boilerfiring fuel used for generating electricity, the management of Consolidated Mining has decided to step up its mining operations. Plans call for increasing the yearly production of steam coal over its current level by: 2te-0.05t million metric tons/year for the next 20 years. The current yearly production is 20 million metric tons. Find a function that describes Consolidated’s total production of steam coal at the end of t years. How much coal will Consolidated have produced over the next 20 years if this plan is carried out?
- Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)A. Find the slope of the curve y = x² - 2x - 4 at the point (2, -4) by finding the limiting value of the slope of the secant line through the point B. Find the equation of the tangent line to the curve at (2, -4)on the chain rule find the tangent line to graph y=(x+2/x+1)^2, at x=0
- Find the slope mm of the tangent line to the parabola f(x)=x^2+7 the point (5, 60) by using the definition: m=limh→0 f(a+h)−f(a)/h m= Find the equation for the tangent line at the point (5, 60), and write it in the form y=mx+b where m = and b =Find the differential eqn. of the ff. family of curves: a.) Straight lines with slope half the value of the x-intercept b.) Circles with center on the y-axis c.) Circles with center on the line y = x, and passing through the originFind an equation of the tangent line to the parabola y = x2 - 6x + 7 at the point (2, -1). SOLUTION From the previous example, we know the derivative of f(x) = x2 - 6x + 7 at the number a is f '(a) = 2a - 6. Therefore the slope of the tangent line at (2, -1) is f '(2) = 2(2) - 6 = . Thus an equation of the tangent line, shown in the figure, is y - ( ) = (x - )or y = x + 3
- A)Determine the equation of the tangent to the curve y = (2x2 – 3) (x + 1)2 at the point wherex = 1. b)Determine the coordinates of the point(s) on the graph of f(x) = where the tangent line is perpendicular to the line 3x + y + 4 = 0.The tangent line to the curve x^3 + y^3 = 9xy at the point (4,2) intersects the y−axis at y=Find an equation of the tangent line to the graph of y = g(x) at x = 2 if g(2) = −3 and g'(2) = 4. (Enter your answer as an equation in terms of y and x.)