As can be read from your statement written "T, equals, start fraction, left parenthesis, d, minus, 15, right parenthesis, strt superscript, 2, end superscript, divided by, 300, end fraction, plus, 20", I hope your model equation is this :
Hope this is your question, if not I think you will, still be able to find an answer of your question based on this solution
As we have to find lowest average temperature, So for minimum of a function its derivative is equal to 0 there.
So lets find derivative of T function first
So first expand as (d-15)(d-15)
we will use FOIL to multiply these
so
so we have
Now we will derivate each term here,300 in denominator is constant so that will come as it in in denominator.
To derivate terms in we will use power rule formula:
so derivative of
Then derivative of d will be 1
so that of -30d will be -30
then derivate of constant -225 will be 0
so we will have derivative as for the fraction part and then derivative of +20 is again 0 as its constant term
For minimum we will put this derivative =0
Now solve for d
times both sides by 300
So now we have to find value of lowest temperature.
For that simply plug 15 in d place in original T function equation
So T = 20 °C is the lowest average temperature and the answer.