Find an equation of the tangent line to the curve at the given point. x? (3,9) (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give the equation in terms of y and x.) equation of the tangent line:

Find an equation to model the vertical motion of the tip of a second hand on a clock, if the second hand is 15cm long. Use t=0 to represent the moment the second hand begins it's cycle at the top of the clock, and let y(t) represent the vertical distance above the center of the clock when t is in seconds. Graph the function, explaining how the values of A,B,C,D each give information about the graph of the function.

Use differentiation to verify each equation. 4x7 d - 1x* - In 1x* + 122 1 + x*

Find the slope of the line tangent to the curve y =x at the point (- 0.4, 0.16) and then find the corresponding equation of the tangent line. The slope is

f(x)=-3x(x+2)^3(x+4) im stuck on how to find the zeros of the function and their multiplicities

In a certain town, the longest day of the year, which is in June, lasts fourteen hours. The shortest day of the year, which is in December, lasts ten hours. Twice per year, in March and September, the day is the same length as the night, or twelve hours. Length of day varies sinusoidally through the year. Write an equation for H(m), the length of the day in hours, as a function of the cosine of m, the number of months since January.

Find the derivative of each function. Can you show me the answer simplified and not simplfied?

Write the given expression as an equivalent function of x that does not involve any trig or inverse trig function.  csc(arcsin(7x/8)=