To find the equation of the tangent line at (2, 2), we need to find the derivative of f(x) first. The derivative of f(x)= alnx+b with respect to x is f'(x) = a/x.
Since we want the tangent line to have a slope of 2, we set f'(2) = 2, and solve for a.
f'(2) = a/2 = 2
a = 4
Now that we have found the value of a, we can substitute it back into the original function and solve for b.
f(x) = alnx + b
f(2) = 4ln2 + b = 2
Solving for b:
4ln2 + b = 2
b = 2 - 4ln2
Therefore, the parameters a and b must equal a = 4 and b = 2 - 4ln2 in order for the line tangent to the curve represented by f(x) at (2, 2) to have a slope of 2.
Suppose you are given the function f(x)=alnx+b . What must the parameters a and b equal so that the line tangent to the curve represented by f(x) at (2,2) has a slope of 2? (1 point) Responses a = 2 and b=2−2ln2 a = 2 and b = 2 − 2 ln 2 a = 2 and b=2−4ln2 a = 2 and b = 2 − 4 ln 2 a = 2 and b=4−2ln2 a = 2 and b = 4 − 2 ln 2 a = 4 and b=2−2ln2 a = 4 and b = 2 − 2 ln 2 a = 4 and b=2−4ln2
1 answer
1 answer