The Sixth GateAfter walking through the fifth gate, your computer informs you that more than half of the gates have beencrossed. "Only 4 left", you conclude. "Computer, what is this gate's riddle?"Your computer responds:42For the function, f (t) = ¼ (2t³ – 15t² + 45 find the value of a that would make the slope of thetangent line -168 at t = 2.a =Explain, in your own words and with your own work, how you arrived at this result. Be sure to explainusing calculus concepts to best support the work of the game design team.

Answered: Image /qna-images/answer/c1686753-562a-4583-94dc-c105d5868704.jpg

=r walking through the fifth gate, your computer informs you that more than half of the gates have been ssed. "Only 4 left", you conclude. "Computer, what is this gate's riddle?" computer responds: 42 the function, f (t) = (2t³ - 15t² +45) find the value of a that would make the slope of the ent line -168 at t = 2. 7= 1 ain, in your own words and with your own work, how you arrived at this result. Be sure to explain g calculus concepts to best support the work of the game design team.