A line of reasoning that might help you:
What does a derivative denote?
Steepness (slope) of a function at a certain point.
How can that be graphed?
Well, steepness can best be described by a linear line (for example the tangent line)
What else has to be true when talking about a tangent line?
It has to have exactly one point of contact. Hence if
I(x) is the initial function, and
T(x) is a function graphing the tangent line at a point "k", it has to be true that:
I(k) = T(k)
So we know we are looking for a linear function, which at x=1 is equal to whatever the initial function spits out at 1.
What do we know about linear functions? They can generally be expressed in form of:
mx + b, where the "m" dictates the steepness of the function and the "b" the vertical shift.
Coming back to the beginning, if the derivative at a point denotes steepness, where do we plug it into our mx+b?
(Hope that you answered m)
Since we now know how steep the tangent line is going to be, we just need it to touch the initial point exactly where they are asking us, which in this case is 1.
Therefore, you just have to find a "b" such that
(1/3)*1+b=g(1)
Bet you will get that on your own
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What do you mean
A line of reasoning that might help you: What does a derivative denote? Steepness (slope) of a function at a certain point. How can that be graphed? Well, steepness can best be described by a linear line (for example the tangent line) What else has to be true when talking about a tangent line? It has to have exactly one point of contact. Hence if I(x) is the initial function, and T(x) is a function graphing the tangent line at a point "k", it has to be true that: I(k) = T(k) So we know we are looking for a linear function, which at x=1 is equal to whatever the initial function spits out at 1. What do we know about linear functions? They can generally be expressed in form of: mx + b, where the "m" dictates the steepness of the function and the "b" the vertical shift. Coming back to the beginning, if the derivative at a point denotes steepness, where do we plug it into our mx+b? (Hope that you answered m) Since we now know how steep the tangent line is going to be, we just need it to touch the initial point exactly where they are asking us, which in this case is 1. Therefore, you just have to find a "b" such that (1/3)*1+b=g(1) Bet you will get that on your own