Explanation:

This question asks for the antonym (opposite meaning) of the word 'Denigrate'. 'Denigrate' means to criticize unfairly; disparage; to speak damagingly of (someone or something); to belittle. \nOption A: 'Malign' means to speak about (someone) in a spitefully critical manner. This is a synonym of 'denigrate', not an antonym. \nOption B: 'Trash' as a verb means to criticize severely or destroy. This is also a synonym or similar in meaning to 'denigrate', not an antonym. \nOption C: 'Endorse' means to declare one's public approval or support of (someone or something). This is the direct opposite of criticizing or disparaging, making it the correct antonym for 'denigrate'. \nOption D: 'Asperse' means to attack the reputation of (someone or something) with damaging remarks; to slander. This is another synonym of 'denigrate', not an antonym. \nTherefore, 'Endorse' is the correct antonym for 'Denigrate'.