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- In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of y = x^2 + 3x + 1. What is the value of k?Use the position fucntion s(t)=-4.9t2+250, which gives the height (in metes) of an object that has fallen for t seconds from a height of 250 meters. The velocity at time t=a seconds given in the picture attached. When will the object hit the ground and at what velocity will the object impact the ground?For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangents to the curve at x=2 and x=3 horizontal?
- For what value or values of the constant k will the curve y = x3 + kx2 + 3x - 4 have exactly one horizontal tangent?For the curve y=ax^3+bx^2+12x-7, what values of a and b will make the tangent to the curve at x=2 and x=3 horizontal?At what point on the parabola y = 3 x2+ 2x is the tangent line parallelto the line y = 10x −2? Use first principles in your solution