Consider the following function. f(x) = -½x2 – 3x + 1
Find the slope and an equation of the tangent line to the graph of the function at the point (-2,5).
Slope: m=
Equation: y =
(Enter equation in slope-intercept form, i.e.y = mx + b)
Consider the function f(x) = x2 - 8x + 8. The slope of the tangent line at x = 5 is 2. Find the equation of this tangent line. (Write your answer in the form y=mx+b with no spaces - as always, if the computer marks you incorrect even if you have the answer correct but just in a different form than I use, email me and I will fix your points.) Given the function f(x)= 4x2 - 3x +...
Find the equation of the tangent line to h(x) = 2 x2 + 3x + 3 at the point (-2,5). y
9. [-14 Points) DET Consider the following. + 7x + 7; Find f'(x). f'(x) = Find F"(-1). f(-1) = Find the slope and an equation of the tangent line to the graph of the function f at the point (-1,-). slope equation y =
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using this definition: The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m=lim x rightarrow a f(x)-f(a)/x-a provided that this limit exists. m = using this equation: m=lim h rightarrow 0 f(a+h)-f(a)/h m= Find an equation of the tangent line in part (a). y...
6. For a certain function f(x) we have: f'(x) = (x - 3)²(2x - 3) and • f"(x) = 6(x - 3)(x - 2) (a) Use f' to find the intervals where f is increasing, the intervals where f is decreasing, the x- coordinates and nature (max, min or neither) of any local extreme values. (b) Use f" to find the intervals where the graph of f is concave up, the intervals where the graph of f is concave down...
(1 point) Suppose that f(x) = (3x + 5). (A) Find an equation for the tangent line to the graph off at x = 2. Tangent line: y = (B) Find the values of a where the tangent line is horizontal. If there are no such values, enter - 1000. Values of x =
1/A/Consider the following.:f(x) = x2 − 4x − 1 Complete the table. (Round your answers to four decimal places.) x 0.9 0.99 0.999 1 1.001 1.01 1.1 f(x) ? Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places. If an answer does not exist, enter DNE.) lim x→1 (x2 − 4x − 1) = ? Can you please explain in clear details,step by...
7. Find an equation of the tangent line to the graph of f(x) = x2 - 2x at (-2,8). Write your answer in the y = mx + b form. (12 points)
Consider the function and the value of a. f(x) = -5 X - 1 a = 3 (a) Use mtan f(a+h) - f(a) = lim to find the slope of the tangent line mtan h0 h = f'(a). = mtan 5 4 (b) Find the equation of the tangent line to fat x = a. (Let x be the independent variable and y be the dependent variable.) »- 3 = (x – 3) x Consider the graph. у 5 x...
Find an equation for the tangent line to the graph of the given function at (4,23). f(x)=x2+7 Find an equation for the tangent line to the graph of f(x)-x+7at (4,23) y = Find an equation for the tangent line to the graph of the given function at (4,23). f(x)=x2+7 Find an equation for the tangent line to the graph of f(x)-x+7at (4,23) y =